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THE    PKOVHTCE 

OP 

METHODS  OF  TEACHING. 

A  PROFESSIONAL  STUDY. 

BY 

JAMES  H.  HOOSE,  A.M.,  PH.D., 

PRINCIPAL    OF  THE    STATE    NORMAL    AND    TRAINING 
SCHOOL,    COBTLAND,    N.   Y., 

Author  of  "Studies  in  Articulation,"  "Notes  on  the  Public  School 

System  of  England  and  Scotland,"  "  Vindication  of  the  free 

School  System,"  "Practical  Suggestions  to  Americans 

Visiting  Europe,"  etc.t  etc. 

WITH  AN  INTRODUCTION 

BY 

CHARLES  W.  BENNETT,  D.D., 

PROFESSOR   OF   HISTORY    AND    LOGIC    IN    SYRACUSE    UNIVERSITY. 


SYRACUSE,  N.  Y.  : 

C.   W.  BARDEEN,   PUBLISHER. 
1886. 


OF  THE 

TIB  17  E  RSI  IT 


COPYRIGHT, 

BY 
J.  H.  HOOSE. 


TO  EDUCATORS 


THIS    STUDY    IS    RESPECTFULLY 


AS    A    CONTRIBUTION 
TO    THE 

PROFESSION  OF   TEACHING. 


PROFESSIONAL  MAXIMS  AND  DEFINITIONS. 

"  In  whatever  line  of  study  distinction  is  sought 
the  advantage  of  good  teaching  is  great."— I.  TOD- 
HUNTER. 

"  A  point  which  I  have  incidentally  brought  for- 
ward deserves  some  consideration  ;  I  mean  the  grad- 
ual decay  in  the  educational  value  of  a  subject  as  it 
falls  into  feebler  hands  to  administer. ' ' — IBID. 

11 1  am  afraid  it  must  be  allowed  that  no  art  of 
equal  importance  to  mankind,  has  been  so  little  in- 
vestigated scientifically  as  the  art  of  teaching." — 
Sm  HENRY  SUMNER  MAINE. 

' '  A  good  principle  not  rightly  understood  may 
prove  as  hurtful  as  a  bad. ' ' — MILTON. 

The  Investigation  of  the  Principles  of  Adjusting 
Subject-matter  to  the  Faculties  and  capabilities  of  the 
learning  Mind — the  Process  of  discovering  Methods 
of  Teaching— constitutes  the  conception  of  the  Sci- 
ence of  Teaching.  (See  §  214.) 

The  Investigation  of  Ways  of  applying  Methods  of 
Teaching  in  practice — The  Invention  of  Modes  of 
Teaching — is  the  conception  of  the  Art  of  Teaching. 
(See  §  215.) 

The  Investigation  of  the  Science  and  the  Art  of 
Teaching  constitutes  the  Profession  of  Teaching. 
(See  §  216.) 


TO  THE  PROFESSIONAL  STUDENT. 

"  The  Thoughtful^  person  considers  carefully,  and 
acts  with  reflection  in  regard  to  the  circumstances  of 
a  case." — C.  J.  SMITH. 

"  When  I  have  a  case  before  me,  I  can't  help  think- 
ing of  it  beforehand,  and  perhaps  feeling  grieved 
too,  afterward,  if  in  any  respect  I  might  have  con- 
ducted it  better.  If  I  am  at  dinner,  the  merriment  or 
the  philosophy  of  the  table-talk  suggests  something, 
which  I  put  away  into  a  pigeon-hole  in  my  mind  for 
the  case  ;  and  when  I  read,  be  it  poetry  or  prose,  the 
case  hangs  over  the  page  like  a  magnet,  and  attracts 
to  itself  whatever  seems  to  be  pertinent  or  applicable. 
Success  or  failure  leaves  a  bright  or  a  dark  hue  on 
my  mind,  often  for  days. "— HORACE  MANN,  Life, 
p.  74. 

' '  There  is  a  certain  reaction  against  the  conserva- 
tism of  scientific  men  at  the  present  time,  and  the 
uneducated  man  believes  that  chance  and  genius  out- 
weigh years  of  the  careful  accumulation  and  sifting 
of  facts.  .  .  It  is,  to  say  the  least,  improbable  at 
this  stage  of  the  world's  progress  that  an  ignorant  or  a 
merely  practical  man  should  discover  a  new  force  in 
Nature.  That  dame  certainly  does  not  put  a  pre- 
mium on  ignorance." — The  Nation,  p.  396,  No.  704, 
Dec.  26,  1878. 

' '  Another  error  is  the  over-early  and  peremptory 
reduction  of  knowledge  into  arts  and  methods  ;  from 
which  time  commonly  sciences  receive  small  or  no 
augmentation.  But  as  young  men,  when  they  knit 
and  shape  perfectly,  do  seldom  grow  to  a  further 


TO  THE   PROFESSIONAL   STUDENT.         VII 

stature  ;  so  knowledge,  while  it  is  in  aphorisms  and 
observations,  it  is  in  growth:  but  when  it  once  is. 
comprehended  in  exact  methods,  it  may  perchance 
be  further  polished  and  illustrated  and  accommo- 
dated for  use  and  practice  ;  but  it  increaseth  no- 
more  in  bulk  and  substance. 

' '  Another  error  which  doth  succeed  that  which  we 
last  mentioned,  is,  that  after  the  distribution  of  par- 
ticular arts  and  sciences,  men  have  abandoned  univer- 
sality, or  philosophia  prima :  which  cannot  but  cease 
and  stop  all  progression.  For  no  perfect  discovery 
can  be  made  upon  a  flat  or  level :  neither  is  it  possi- 
ble to  discover  the  more  remote  and  deeper  parts  of 
any  science,  if  you  stand  but  upon  the  level  of  the 
same  science,  and  ascend  not  to  a  higher  science." — 
BACON,  Advancement  of  Learning,  pp.  39,  40,  Ed. 
1866,  Oxford. 


A  LIST  OF  AUTHORS  AND  WORKS  QUOTED  IN 
THIS  VOLUME. 


John    W.    Armstrong,    D.D.— "On    Method"    (An 
Article). 

Thomas  Arnold,  D.D. — "Life  and  Correspondence," 
by  Arthur  P.  Stanley,  M.A. 

"  The  Art  Journal." — Monthly,  New  York. 

Charles  W.  Bennett,  D.D.— "  History  of  the  Philos- 
ophy of  Pedagogics." 

Alexander  Bain,  M.A. — Article  in  "  Mind." 

"  A  Brief   English  Grammar  on   a    Logical 

Method." 

'  Senses  and  Intellect." 


Francis  Bacon. — <l  Advancement  of  Learning." 
Joseph  Bosworth,   D.D.,  F.R.S.,  F.S.A.—  "A  Com- 
pendious Anglo-Saxon  and  English  Dictionary." 
Wilhelm  Adolf  Becker.—"  Charicles,"  translated  by 

Frederick  Metcalfe,  M.A. 
Francis  Bowen,  LL.D. — "A  Treatise  on   Logic;  or, 

The  Laws  of  Pure  Thought." 
M.  Bautain,  Professor  at  the  Sorbonne. — "The  Art 

of  Extempore  Speaking." 

Joseph  Butler,  D.C.L. — "  The  Analogy  of  Religion." 
Henry  Calderwood,  LL.  D. ,  F.  R.  S.  E.  — < '  On  Teaching : 
Its  Ends  and  Means." 

"  Hand-Book  of  Moral  Philosophy." 

Chambers'  Encyclopaedia. 
Henry  Coppee,  A.M. — "  Elements  of  Logic." 
George  Crabb,  M.A. — "English  Synonyms." 
B.  F.  Cocker,  D.D.,  LL.D.— "  The   Theistic  Concep- 
tion of  the  World." 

Henry  N.  Day,  LL.D.—"  Elements  of  Logic." 
"Outlines  of  Ontological  Science." 


LIST   OF   AUTHORS   AKD   WORKS.  IX 

Dayies  and  Peck—"  Dictionary  of  Mathematics." 

Epictetus — "Discourses  translated  by  George  Long." 

English  Cyclopaedia— Ed.  1867. 

William  Fleming,  D.D.— "  The  Vocabulary  of  Phi- 
losophy. " 

Leo  H.  Grindon — ' '  Life. " 

Thomas  Henry  Huxley,  LL.D.,  F.R.S.— "  Lay  Ser- 
mons, Addresses,  and  Reviews." 

Thomas  Hill,  LL.D.—"  The  True  Order  of  Studies." 

Levi  Hedge,  LL.D. — "  Elements  of  Logick." 

Sir  William  Hamilton — "  Metaphysics." 

W.  Stanley  Jevons,  LL.D.,  M.A.,  F.R.S.— Article  in 
"Mind." 

"  The  Principles  of  Science." 

"Elementary  Lessons  in  Logic." 

William  James — Article  in  "  Mind." 

Dionysius  Longinus — "On  the  Sublime,"  translated 
by  William  Smith. 

S.  S.  Laurie,  A.M. — "  Inaugural  Address — Chair  of 
Education  in  University  of  Edinburgh." 

"Synopsis  of  Lectures." 

Horace  Mann— "  Life,"  by  his  Wife. 

"  Mind  " — A  Quarterly — London. 

J.  D.  M.  Meiklejohn,  M.A. — "Inaugural  Address, 
Bell  Chair  of  Education,  University  of  St. 
Andrews." 

J.  Clark  Murray—"  Outlines  of  Sir  William  Hamil- 
ton's Philosophy." 

John  Stuart  Mill — "  A  System  of  Logic,  Ratiocinative 
and  Inductive ;  being  a  Connected  View  of  the 
Principles  of  Evidence  and  the  Method  of  Scien- 
tific Investigation." 

Michael  Seigneur  De  Montaigne — "  Essays." 

Sir  Henry  Sumner  Maine,  R.C.S.Q.,  LL.D.,  F.R.S.— 
"Village  Communities  and  Miscellanies." 

L.  Mariotti — "Conferences  De  Pedagogic." 

Henry  Longueville  Mansel,  B.D. — "  Metaphysics." 

"Prolegomena  Logica." 

James  McCosh,  LL.D. — "Intuitions  of  the  Mind." 


X  LIST   OF   AUTHOES   AND   WOKKS. 

John  Ferguson  McLennan,  M. A.,  LL.D."— "  Primi- 
tive Marriage/' 

J.  H.  Newman,  M. A. — "The  Idea  of  A  University." 

"  The  Nation"— A  Weekly— New  York. 

David  P.  Page,  M.A.—"  Theory  and  Practice  of 
Teaching." 

Noah  Porter,  D.D. — "  The  Human  Intellect." 

Jean  Paul  Frederick  Richter — "Levana." 

Karl  Rosenkranz — "  The  Philosophy  of  Education, 
or  Pedagogics  as  a  System,"  translated  by  Anna 
C.  Brackett. 

Jean  Jacques  Rousseau — "  Emilius  and  Sophia,"  4 
vols.  Ed.  1783.  London. 

James  E.  Thorold  Rogers,  M.A. — "  Education  in 
Oxford." 

Laurence  Sterne — "  Life  and  Opinions  of  Tris  tram 
Shandy." 

Karl  Schmidt — Quoted  by  Dr.  Bennett. 

Henry  Sidgwick,  M.A. — "  The  Methods  of  Ethics." 

C.  J.  Smith — "Synonyms  Discriminated." 

Herbert  Spencer — "  Education." 

J.  A.  Stewart— Article  in  "  Mind." 

Sydney  Smith — "Essays." 

Louis  Sol  dan — "  Method  and  Manner,"  in  Transac- 
tions of  Nat.  Ed.  Association  for  1874. 

James  Fitzjames  Stephen,  Q.C. — "Liberty,  Equality, 
Fraternity." 

I.  Todhunter,  M.A.,F.R.S.—"  The  Conflict  of  Studies, 
and  other  Essays." 

Edward  B.  Tylor,  LL.D.,  F.R.S.— " Primitive  Cul- 
ture," 2  volumes. 

William  Thompson,  D.D. — "  An  Outline  of  the 
Necessary  Laws  of  Thought." 

Frederick  Ueberweg — "  System  of  Logic,  and  History 
of  Logical  Doctrines,"  translated  by  Thomas  M. 
Lindsay,  M.A.,  F.R.S.E. 

Varro— Quoted  by  Rousseau. 

William  Whewell,  D.D. — "  Novum  Organon  Reno- 
vattim." 

Richard  Whately — "  Elements  of  Logic." 


PREFACE. 


THE  following  STUDY  has  grown  out  of  one  branch 
of  the  investigations  which  have  occupied  my  time 
more  or  less  during  an  extended  period  of  years  of 
public  labors  in  teaching.  This  volume  has  gradually 
assumed  form  for  my  own  classes  in  professional  re- 
searches. I  have  been  impressed  long  with  the 
thought  that,  as  teachers  and  educators  of  the  United 
States,  we  are  top  impatient  and  superficial  in  our  pro- 
fessional inquiries.  The  consequences  are,  that  our 
theories  of  teaching  rest  too  heavily  upon  notions  of 
present  expediency  and  brief  experience.  As  a  body 
we  are  in  full  sympathy  with  the  general  spirit  of  the 
nation — we  are  satisfied  with  only  immediate  results. 
Parents  urge  us  to  hasten  their  children  into  the 
mysteries  of  learning,  for  soon  they  must  be  placed 
at  work,  or  must  enter  the  advanced  schools.  The 
legitimate  consequences  are  at  pur  doors :  the  cry 
of  the  upper  schools  is,  that  candidates  for  admission 
are  too  poorly  prepared  for  the  work  in  store  for 
them ;  the  experienced  men  of  business  complain 
that  the  youth  are  not  properly  grounded  in  the  prin- 
ciples underlying  their  daily  routine  of  labors  ;  the 
educated  unite  in  proclaiming  the  masses  uneducated. 
Thus  have  we  been  between  these  upper  and  nether 
millstones,  crushed  and  thrown  out  if  immediate 
scholarship  was  not  forthcoming,  while  we  are  cen- 
sured in  after-years  for  not  having  secured  more  valu- 
able products  for  the  study  expended  by  the  children 
in  their  early  school-days. 


Xll  PREFACE. 

In  this  dilemma  we  have  recollected  the  wisdom  of 
the  Dutch  proverb,  ''Economy  is  a  great  revenue," 
and  the  German,  "  Necessity  teaches  even  the  lame 
to  dance,"  and  the  Italian,  "  Even  the  dog  gets  bread 
by  wagging  his  tail,"  and  have  endeavored  to  insure 
to  the  pupils  a  scholarship  that  is  frequently  too  in- 
sufficient to  be  valuable,  but  which  has  secured  for 
us  an  ephemeral  reputation  and  a  jeopardized  sup- 
port. Under  all  the  circumstances,  perhaps  we  have 
done  as  Avell  as  we  could  in  our  schools. 

Because  we  have  yielded  so  far  to  the  popular  de- 
mands, we  are  to-day  without  a  sharply  defined  and 
outlined  philosophy  in  our  theories  of  education  and 
of  teaching.  In  our  experimentation  for  sudden 
fruitage  we  have  apparently  forgotten  that  the  most 
practical  thing  in  existence  is  a  thoroughly  matured 
philosophical  theory.  Experiments  without  this 
theory  are  at  random  ;  they  may  be  successful — 
probably  they  will  not  be.  Under  a  correct  theory, 
experiments  can  be  tested  philosophically,  and  fail- 
ures reduced  to  a  minimum  in  number  and  in  degree 
of  disaster.  In  this  respect  we  can  learn  much  from 
those  nations  that  have  passed  their  eager  and  experi- 
mental age,  and  are  now  in  their  enlightened  matur- 
ity. In  our  ambition  to  "  make  scholars,"  irrespec- 
tive of  the  elements  of  necessary  time  and  applica- 
tion, we  have  overlooked  the  fact  that  scholars  can 
never  be  "made;"  they  must  grow:  the  faculties 
become  powers  only  as  time  and  application  enucleate 
them.  The  active  energies  of  the  Profession  have 
been  too  much  absorbed  in  inventing  artificial  aids, 
helps,  short-cuts,  and  "royal  roads"  to  learning,  to 
enter  into  patient  and  continued  study  to  discover 
the  philosophical  nature  of  the  Profession  as  an  Art 
and  as  a  Science.  It  is  time  for  us  to  turn  our  atten- 
tion to  find  a  firmer  basis  for  our  practice.  This  is 
found  only  in  Philosophy. 

"  The  beginning  of  philosophy  to  him  at  least  who 
only  enters  on  it  in  the  right  way  and  by  the  door,  is 


PREFACE.  X11I 

a  consciousness  of  his  own  weakness  and  inability 
about  necessary  things. "— EPICTETUS. 

The  work  now  submitted  is  an  attempt  to  outline 
one  subject  which  is  included  within  the  conception 
of  a  complete  Philosophy  of  Education — that  of  the 
Province  of  Methods  of  Teaching.  Although  the  sub- 
ject is  not  first  in  the  order  of  classification  in  the 
general  investigation  of  Education,  yet  because  of  its 
practical  nature  it  has  been  directly  approached. 

The  treatment  is  somewhat  out  of  the  ordinary 
mode  of  authorship.  While  I  have  steadily  kept  to  the 
line  of  the  investigation,  yet  I  have  permitted  a  wide 
range  of  related  matter  to  incorporate  itself  into  the 
body  of  the  text,  even  at  the  risk  of  seeming  to  be 
pedantic.  The  disadvantages  of  this  apparent  hetero- 
geneity are  more  than  compensated  by  the  greater 
suggestiveness  of  the  materials  admitted.  Besides,  he 
who  would  erect  a  "  liberty- pole"  that  shall  remain 
permanently  standing  as  a  beacon  must  imbed  it  deep- 
ly into  the  firmest  of  soil  which  the  past  and  present 
have  deposited  from  the  attrition  of  the  Ages. 

' '  The  reader  will  please  to  take  it  patiently  if  he  find 
what  has  been  already  printed  again  printed  here. 
What  has  been  printed  is  necessary  as  the  bond  and 
bast-matting  of  what  has  not  been  printed  ;  but  the 
bast-matting  must  not  cover  the  whole  garden,  in- 
stead of  merely  tying  up  the  trees.  But  there  are 
two  still  better  excuses.  Known  rules  in  education 
gain  new  force  if  new  experience  verifies  them.  The 
author  has  three  times  been  in  the  position  of  trying 
them  upon  different  children  of  all  ages  and  talents  ; 
and  he  now  enjoys  with  his  own  the  pedagogic  jus 
trium  liberorum  (law  of  three  children) ;  and  every 
other  person's  experience  related  in  this  book  has  been 
made  his  own.  Secondly,  printing-ink  now  is  like 
sympathetic  ink,  it  becomes  as  quickly  invisible  as 
visible  ;  wherefore  it  is  good  to  repeat  old  thoughts 
in  the  newest  books,  because  the  old  works  in  which 
they  stand  are  not  read.  New  translations  of  many 
truths,  as  of  foreign  standard  works,  must  be  given 


XIV  PREFACE. 

forth  every  half  century.  And,  indeed,  I  wish  that 
even  old  German  standard  books  were  turned  into 
new  German  from  time  to  time,  and  so  could  find 
their  way  into  the  circulating  libraries. 

"  Why  are  there  flower  and  weed  gleanings  of 
every  thing,  but  no  wine  or  corn  gleanings  of  the  in- 
numerable works  on  education?  Why  should  one 
single  good  observation  or  rule  be  lost  because  it  is 
imprisoned  in  some  monstrous  folio,  or  blown  away 
in  some  single  sheet  ?  For  dwarfs  and  giants,  even 
in  books,  do  not  live  long.  Our  age,  this  balloon,  or 
air- ship,  which,  by  simultaneous  lighting  of  new 
lamps,  and  throwing  out  of  old  ballast,  has  constantly 
mounted  higher  and  higher,  might  now,  I  should 
think,  cease  to  throw  out,  and  rather  lovingly  en- 
deavor to  collect  than  to  disperse  the  old. 

"  However  little  so  disjointed  a  collection  of 
thoughts  could  teach  rules,  it  would  yet  arouse  and 
sharpen  the  educational  sense,  from  which  they  orig- 
inally sprung 

1 '  Something  very  different  from  such  a  progressive 
cabinet  of  noble  thoughts,  or  even  from  my  weak 
Levana,  with  her  fragments  in  her  arms,  is  the  usual 
kind  of  complete  system  of  education  which  one 
person  after  another  has  written,  and  will  write. 
It  is  difficult, — I  mean  the  end,  not  the  means. 
For  it  is  very  easy  to  proceed  with  book-binder's  and 
bookmaker's  paste,  and  fasten  together  a  thousand 
selected  thoughts  with  five  of  your  own,  especially  if 
you  conscientiously  remark  in  the  Preface  that  you 
have  availed  yourself  of  the  labors  of  your  predeces- 
sors, yet  make  no  mention  of  one  in  the  work  itself, 
but  sell  such  a  miniature  library  in  one  volume  to 
the  reader  as  a  mental  fac-simile  of  yourself.  How 
much  better  in  this  case  were  a  hole-maker  than  a 
hole-hider  !  How  much  better  were  it  if  associated 
authors  (I  mean  those  friendly  hundreds  who  move 
along  one  path,  uttering  precisely  the  same  sound) 
entirely  died  out — as  Humboldt  tells  us  that  in  the 
tropical  regions  there  are  none  of  those  sociable 


PREFACE.  XT 

plants  which  make  our  forests  monotonous,  but  next 
each  tree  a  perfectly  different  one  grows.  A  diary 
about  an  ordinary  child  would  be  much  better  than 
a  book  upon  children  by  an  ordinary  writer.  Yes, 
every  man's  opinion  about  education  would  be  valu- 
able if  he  only  wrote  what  he  did  not  copy.  The 
author,  unlike  a  partner,  should  always  only  say 
'I,'  and  no  other  word."— JEAN  PAUL  RICHTER. 
Levana,  Author's  Preface,  pp.  xii-xv,  ed.  1863. 

Although  Methods  of  Teaching  occupied  the  atten- 
tion of  some  of  the  Greek  philosophers,  and  have  con- 
tinued before  the  minds  of  educators  in  portions  of 
Europe  down  to  the  present  date,  and  have  of  late 
engaged  thought  in  the  United  States,  yet  they  have 
been  confounded  generally  with  Methods  of  Educa- 
tion, Modes  and  Manners  of  Teaching,  rather  than 
apprehended  as  constituting  a  province  by  them- 
selves. The  subject  of  the  inquiry  being  intricate 
in  its  character,  it  has  been  no  easy  task  to  elaborate 
it.  I  have  diligently  sought  nothing  but  Truth. 
Should  subsequent  researches,  observations,  or  ex- 
perience, from  whatever  source,  reveal  aught  of  error 
in  the  positions  advanced,  no  one  shall  outdo  the 
author  in  haste  to  accept  the  facts  as  they  shall  ap- 
pear. If  this  investigation,  with  all  of  its  imperfec- 
tions of  style,  matter,  and  treatment,  shall  prove  as 
interesting  to  the  Fraternity  as  it  has  to  the  writer, 
it  will  serve  its  purpose.  "  Indeed,  its  largeness, 
its  infinity,  embarrass  me.  It  is  like  an  attempt  to 
lift  the  earth  :  the  arms  are  too  short  to  get  hold  of  it. 
However,  I  hope  to  get  hold  of  a  few  handfuls." 
HORACE  MANN,  Life,  p.  87,  Boston,  1865. 

<4 1  have  long  known  that  no  man  can  apply  himself 
to  any  worthy  subject,  either  of  thought  or  action, 
but  he  will  forthwith  find  it  develop  into  dimensions 
and  qualities  of  which  before  he  had  no  conception. 
If  this  be  true  of  all  subjects  worthy  of  rational  at- 
tention, how  extensively  true  is  it  of  the  all-compre- 
hending subject  of  education  !  This  expansion  of 
any  object  to  which  our  attention  is  systematically 


XVI  PREFACE. 

directed  may  be  compared  to  the  opening  of  a  con- 
tinent upon  the  eye  of  an  approaching  mariner.  At 
first  he  descries  some  minute  point,  just  emerging  in 
fhe  distance, — the  lofty  summit  of  some  mountain. 
As  he  approaches,  other  elevated  points  seem  to  rise 
out  of  nothing,  and  stand  upon  the  horizon  ;  then 
they  are  perceived  to  be  connected  together  ;  then 
hills,  cities,  towns,  plains,  rivers,  which  the  eye  can- 
not count  for  their  numbers,  nor  embrace  for  their 
distance,  fill  up  the  admiring  vision.  So  it  is  in  ap- 
proaching any  of  the  intellectual  or  moral  systems 
which  Nature  has  established.  "—Ibid. ,  pp.  84,  85. 

J.  H.  H. 


ANALYTICAL  TABLE  OF  CONTENTS. 


PAGE 

DEDICATION iii 

PROFESSIONAL  MAXIMS v 

To  THE  PROFESSIONAL  STUDENT vi-vii 

A  LIST  OF  AUTHORS  AND  WORKS  QUOTED viii-x 

PREFACE xi-xvi 

TABLE  OF  CONTENTS xvii-xxx 

INTRODUCTION— By  Dr.  Charles  W.  Bennett xxxi-xxxvii 


ANALYTICAL  TABLE  OF  CONTENTS. 


PAET   FIRST. 

INTRODUCTORY   DISCUSSION  —  On   Pedagogics,   Education, 
Teaching,  Authorities 

I.  ON  PEDAGOGICS. 

SECTION  PAGE 

1.  Pedagogics— definition  of From  Soldan  3 

2.  Pedagogics— definition  of From  Rosenkranz  4 

3.  Pedagogics— definition  of From  Schmidt,  quoted  by 

Bennett  4 

II.  ON  EDUCATION. 

4.  Education— province  of 5 

5.  Education— province  of From  Rousseau  5 

6.  Education — province  of From  Rosenkranz  6 

7.  Education— province  of From  Rogers  9 

8.  Education— province  of From  Bain  9 

9.  Education— province  of From  Jevons  20 

10.  Education— province  of  From  Varro  22 

11.  Education  and  Training From  Smith  2*2 

12.  Education— province  of « From  Hill  23 

13.  Education — province  of From  Page  24 

14.  Education— province  of From  Huxley  26 

15.  Education— province  of From  Laurie  30 

16.  Education— province  of From  Richter  34 

17.  Education  vs.  Instruction From  Richter  42 

18.  Education  vs.  Teaching 43 

19.  Education  vs.  Teaching From  Caldenvood  43 


ANALYTICAL  TABLE  OF  CONTENTS.       Xix 
III.  ON  TEACHING. 

SECTION  PAGE 

SO.  Language— represents 44 

21.  Teaching — meaning  of From  the  Greek  45 

22.  Teaching — meaning  of From  the  Latin  47 

23.  Teaching— meaning  of From  the  Anglo-Saxon  49 

24.  Methods  of  Teaching— expression  determined 50 

25.  Authority  in  Anglo-Saxon  Conception  of   Teaching- 

illustrated From  Todhunter  51 

26.  Same  idea— illustrated From  Jevors  51 

27.  Same  idea— illustrated From  Caldenvood  52 

28.  Conception  of  Teacher  limited  to  Persons 54 

29.  Teach,  Instruct,  Inform— defined From  Crabb  55 

30.  Teach,  Instruct,  Inform— defined From  Smith  57 

IV.  ON  AUTHORITIES. 

31.  Authority— denned From  Crabb  60 

32.  Authority— defined From  Smith  60 

33.  Authority,  Consent,  Assent,  Belief— defined. 

From  Fleming  61 

34.  Authority— general  discussion From  Bacon  69 

35 V.  RECAPITULATION 77 


PART    SECOND. 

ON  METHOD  IN  GENERAL. 

36.  Method— defined 79 

37.  Method— refers  to  subject-matter 80 

38.  Methods  of  Business— customary  use  of  Expression 80 

39.  Methods  of  Business— illustrated.  .From  li  The  Nation  "  81 

40.  Three  distinct  Elements  in  an  Investigation— (1)  Object- 

matter,  the  end ;   (2)  Way  in  which  faculties  pro- 
ceed ;  (3)  State  of  Investigator 82 

41.  I.  Object-matter  of  Study— considered— ends  in  System.    83 

42.  II.  Ways  of  Procedure  of  Mind— considered— Are  modes 

of  method 85 

43.  (a)  Analysis— defined 85 


XX        ANALYTICAL  TABLE  OF  CONTENTS. 

SECTION  PAGE 

44.  Analysis  vs.  Separation 86 

45.  (b)  Synthesis— defined 87 

46.  Synthesis  and  Definition 87 

47.  Abstraction— defined 87 

48.  Analysis  and  Synthesis  are  parts  of  same  Method. 

From  Hamilton  87 

49.  Synthesis  vs.  Reconstruction 88 

50.  (c)  Generalization— defined 89 

51.  (d)  Classification— defined 89 

52.  (e)  Induction—  defined 90 

53.  Induction  vs.  Interpretation 90 

54.  Induction  vs.  Repetition 92 

55.  (/)  Deduction— defined 93 

56.  HI.  State,  or  Ways  of  Investigator— give  rise  to  Manner.  93 

57.  Manner  Systematized  is  Mode 94 


PART   THIRD. 

I.  ON  THE  THEORY  OF  METHODS  OP  TEACHING. 

58.  Introduction—Need  of  Better  Methods From  Maine    96 

59.  Theory  of  Methods  of  Teaching— hased  upon  Psychology 

and  nature  of  subject-matter 98 

60.  Nature  of  Faculty— defined 98 

61.  Character  of  Faculty— defined. 98 

62.  Psychology— defined 98 

63.  Psychology— province  of From  Stewart    98 

64.  Objects  and  Limitations  of  Present  Investigation 101 

65.  Knowing— forms  of  knowledge From  Ueberweg  102 

66.  Form  and  Matter From  Thompson  103 

67.  Form  and  Matter From  Jevons  105 

68.  Form  and  Matter From  McCosh  105 

69.  Form  and  Matter From  Newman  107 

70.  Form  of  Matter— (a)  Illustrated. .  .From  "The  Nation11 

(o)  Illustrated From  Rousseau  107 

71.  Knowledge,  Learning,  Erudition— defined.. From Crabb  108 


ANALYTICAL  TABLE  OF  CONTENTS.       Xxi 

SECTION  PAGE 

72.  Knowledge— defined From  Day  110 

73.  Knowledge — defined From  Day  111 

74.  Knowledge— aim  of,  is  truth From  Ueberweg  112 

75.  Knowledge— stages  of,  in  acquiring  :  (1)  Source  of— re- 

sides in  mind  ;  (2)  Rational  way  of  procedure  is 
under  Will ;  (3)  End  of  activity  is  Knowledge 113 

76.  Teaching— defined 114 

77.  Self-Informed  is  Self-educated— defined  and  amplified. . .  114 

78.  Teachers  are  a  Necessity  to  Learners — Teacher,  what  is 

—Adjust,  defined From  Smith  115 

79.  Teaching— defined 116 

80.  Teacher— duties  of,  to  analyze  and    separate  subject- 

matter  117 

81.  Teacher— duty  to  note  both  form  and  matter  of  knowl- 

edge in  mind  of  learner 117 

82.  How  to  Teach  ?— is  great  question 118 

83.  Teaching— Conception  of,  requires  examination  of  :   (1) 

Mind  of  learner— learner ;  (2)  Mind  of  teacher- 
teacher  ;  (3)  Things  to  be  learned— subject-matter. .  118 

84.  Teaching — Conception  of,  resolves  itself  into:  (1)  Teacher 

must  know  subject-matter  ;  (2)  Teacher  must  know 
mind  ;  (3)  Teacher  must  know  Way  in  which  mind 
proceeds  when  learning— Constitute  Profession  of 
Teaching 119 

85.  Recapitulation  of  §§  82,  83 120 

86.  PROVINCE  OF  METHODS  OF  TEACHING— that  of  Princi- 

ples of  Adaptation  of  Subject-matter  to  Faculties  of 
Mind 121 

87.  Principle— defined From  Fleming  122 

88.  Principle— defined. . .  From  Smith  122 

89.  Methods  of  Teaching — require  system  of  subject-matter.  123 

90.  Systems  and  Methods— compared 123 

91.  Province  of  Methods  of  Teaching,  not  that  of  Pedagogics 

or  Ethology 125 

92.  Ethics— defined . . .-. From  Sidgwick  125 

93.  Teaching  is  Handmaid  of  Education. 126 

94.  Methods  of  Pedagogics,  Scope  of — equivalent  to  Meth- 

ods of  Education 127 


XX11     ANALYTICAL  TABLE  OF  CONTENTS. 

SECTION  PAGE 

95.  Methodick  of  Education— defined.   (1)  Educator  must  be 

a  Guide— Processes  :  Analytic,  Synthetic,  Inductive. 
(2)  Educator  must  guide  Morals— Methodick  of  Edu- 
cation is  Methodology,  Way,  Procedure— Method- 
ick—rests  on  the  Will.  Departments  of— particu- 
lar methods From  Laurie  129 

96.  Methods  of  Education  regard  Growth  of  Mind  as  an 

End— They  consider  :  (1)  What  Subjects  to  be 
Taught— purpose  of.  (2)  How  to  Instruct  for  Right 
Judgments.  Answers :  To  (1)  Doctrine  of  the  Real— 
To  (2)  Formal  Discipline From  Laurie  131 

97.  Growth  and  Development— contrasted...  From  Spencer  132 
Growth— defined From  Smith  132 

98.  Methods  of  Teaching  regard  Growth  of  Mind  as  a  Means  135 

99.  Methods  of  Teaching  Examined  in  their  Relation  to 

"  How  to  Study  " 136 

100.  Methods  of  Teaching  do  not  distinguish  between  Truth 

and  Error  of  Subject-matter  taught 138 

101.  Methods  of  Teaching  assume  innate  Activity  of  Mind- 

Examined  in  relation  to  "  Waking  up  Mind"— Con- 
ception of  "  Variety"  examined 139 

102.  Attention— defined  and  examined From  Richter  139 

103.  Excite,  Awaken,  Rouse,  Incite,  Stimulate— defined. 

From  Smith  141 

104.  Methods  of  Teaching— not  responsible  for  Form  of 

Knowledge  in  Mind  of  Learner 142 

105.  "  Development  of  Ideas11— analyzed 144 

1l06.  Thorough  Teaching— defined 144 

107.  Develop,  Unfold,  Unravel— defined From  Smith  145 

108.  Methods  of  Teaching  must  regard  Procedure  of  Facul- 

ties when  learning. .  148 

109.  Methods  of  Discovery  and  of  Instruction. From  Jevons  149 

110.  Methods  of  Teaching  must  respect  Inherited  "Cast  of 

Mind" 160 

111.  Methods  of  Teaching— difficult  to  suit,  because  of  evan- 

escence of  psychological  phenomena 162 

112.  Methods  of  Teaching— in  present  state  of  Psychology, 

not  absolutely  invariable 163 


ANALYTICAL  TABLE  OF  CONTENTS,    xxiii 

SECTION  PAGE 

113.  Methods  of  Teaching  examined  in  relation  to  "  Class- 

Drill" 164 

114.  Methods  of  Teaching  do  not  regard  Individuality  of 

Teacher 165 

115.  Manner— Examined  and  defined 165 

116.  Teacher  can  have  "His Manner,"  not  "His  Method".  166 

117.  Methods  of  Teaching— are  not  method  in  general . .  166 

118.  Method  and  Manner— contrasted From  Soldau  167 

119.  Mode  of  Teaching— defined 168 

120.  Methods,  Modes,  Manners— compared 168 

121.  In  Perfect  Knowledge,  all  Teachers  would  Teach  alike 

in  their  Modes 169 

122.  Methods  of  Teaching— Misconception  of  occasions  Mis- 

use of  the  Expression 170 

123.  Mode,  Manner— defined From  Smith 

Mode,  Manner— used From  "  The  Nation"  171 

124.  System,  Method— defined From  Smith 

System— defined From  Jevons  172 

125.  Method,  Procedure— defined From  Mariotti  172 

126.  Method,  Mode— defined From  Armstrong  173 

127.  Principle,  Law,  Rule— defined From  Armstrong  173 

128.  Method,  Mode,  Manner— difference,    (a)  Illustrated  by 

Figure  of  a  Bridge;  (ft)  Illustrated  by  Water  as 
buoying-up  power ;  (c)  Illustrated  by  Gravity,  Ani- 
mal Power,  Steam  ;  (tf)  Illustrated  by  Horse  Power, 
Carriage,  Landau v 174 

129.  Mode— properly  used From  Page  175 

130.  Mode  of  Teaching— illustrated From  Page  175 

131.  Method— improperly  used From  Rousseau  176 

132.  Method— Socratic  Mode— illustrated. .  .From  Epictetus  178 

133.  Methods  of   Teaching— for  Modes  and  Manners— Cri- 

tique upon From  Meiklcjohn  184 

134.  "Methods   of  Nature"— Conception    of,  Examined— 

Illustration From  Rousseau 

Illustration From  McLennan  188 

135.  Artificial— Conception  of,  examined 190 

136.  Natural,  in  general,  is  not  Natural  in  the  Individual.. . .  192 

137.  Natural— defined ...  From  Butler  193 


XXiv    ANALYTICAL  TABLE  OF  CONTENTS. 

SECTION  PAGE 

138.  Nature— defined From  Cocker  193 

139.  Nature— Law  of— defined From  Cocker  194 

140.  Nature— Universality  of  Order  of— defined— not  Inva- 

riable  From  Cocker  194 

141.  Nature— defined From  Fleming  196 

142.  Natural— Instance  of From  Epictetus  200 

143.  Natural  and  Artificial  Education— discriminated. 

From  Huxley  202 

II.  ON  THE  PRACTICE  or  METHODS  or  TEACHING. 
(A)  On  the  Knowing  Faculties  of  the  Mind. 

144.  Purpose  of  this  Division  is  to  submit  a  Basis  for  Meth- 

ods of  Teaching 203 

145.  Psychological  Phenomena— classified.    (1)  Phenomena 

of  Cognitions  ;  (2)  Phenomena  of  Feelings  ;  (3)  Phe- 
nomena of  Conations From  Hamilton  204 

146.  Consciousness— defined.  Involves :  (1)  A  Knowing  Sub- 

ject, the  Ego ;  (2)  A  Recognized  Modification  of 
Ego  ;  (3)  A  Recognition  by  the  Subject  of  the  Modi- 
fication  (a)  From  Hamilton 

(b)  From  James  204 

147.  I.  Presentative  Faculties From  Hamilton  205 

148.  II.  Memory— Faculty  of From  Hamilton  207 

149.  III.  Reproductive  Faculty From  Hamilton  207 

150.  IV.  Imagination From  Hamilton  208 

151 .  -V.  Elaborative  Faculty From  Hamilton  208 

152.  VI.  Regulative  Faculty. . .! From  Hamilton  209 

153.  Recapitulation  of  Cognitive  Faculties.  .From  Hamilton  210 

154.  Will,  the  Principal  Faculty  in  acquiring  Knowledge. 

From  Richter  211 

155.  Will— same  idea From  Laurie  213 

156.  Will— same  idea From  Cocker  213 

157.  Imagination— (a)  The  Poetic From  Porter  214 

158.  Imagination— 0)  The  Philosophic From  Porter  214 

159.  Imagination— (c)  The  Ethical  Uses  of From  Porter  216 

160.  Imagination— (d}  Relation  to  Religious  Faith. 

From  Porter  217 

161.  Imagination  is  Over-developed  in  the  Youth  of  India. 

From  Maine  218 


ANALYTICAL  TABLE  OF  CONTENTS.       XXV 

SECTION  PAGE 

105.  Memory— Modification— defined 219 

163.  Memory — Active — Childhood  need  not  Understand  all 

it  Learns From  Arnold  219 

164.  Memory,  Imagination,  and  Hope  are  the.same  Faculty. 

From  Hansel  220 

165.  Memory— Permanence  of From  Grindon  221 

166.  Memory— Limited  in  its  Growth From  Richter  224 

167.  Memory— Eetains  best  from  Contrasts ...  From  Kichter  226 

168.  Memory— a  Goddess From  Montaigne  227 

169.  Memory— a  Personal  Reminiscence — From  Montaigne  227 

170.  Memory  and  "  Cram" From  Maine  235 

171.  Memory  and  "  Cram" From  Todhunter  240 

172.  Memory  and  "Cram,"    and    Thinking  Faculties — A 

Question-Begging  Epithet;  Analysis  of  "Cram;" 
"Good  Cram"  and  ; 'Bad  Cram"  defined  ;  Dulness 
and  'Cram;"  Book- work  and  "Cram;"  Exami- 
nations are  Tests  ;  Repetition  in  Teaching  Neces- 
sary;  Purpose  of  "Good  Cramming;"  Intense 
u Cramming"  is  Real  Education;  Remarks  of 
Home-Secretary  Cross  ;  Mr.  Cross  Answered  ;  Slow 
and  Deliberate  Teaching  compared  with  Rapid; 
Object  of  School  ;  Purpose  of  Liberal  Education ; 
Not  Desirable  to  Remember  things  Taught  in 
School ;  Source  of  Error  not  in  Memory,  but  in 
Distinguishing  between  Form  and  Matter;  Reten- 
tion ;  Barristers  must  Forget ;  Work  of  Teachers 
not  to  make  Philosophers,  and  Scholars,  and  Ge- 
niuses—these are  Born  ;  Business  of  Educator  is 
"  to  Cram" From  Jevons  241 

173.  Knowing,  Act  of— defined From  Ueberweg  257 

174.  Knowledge— defined From  Ueberweg  258 

175.  Human  Thought— determined From  Ueberweg  258 

176.  Knowledge— Activity  necessary  to From  Ueberweg  258 

177.  Knowledge— defined From  Calderwood  259 

178.  Thought— Difference  between,  and  other  Phenomena 

of  Mind  —  Intuition,  Conception,  Concept,  Con- 
sciousness, Representation,  Perception,  Imagina- 
tion  From  Mansel  259 


XXVI       ANALYTICAL  TABLE  OF  CONTENTS. 

SECTION  PAGE 

179.  Thought— defined From  Mansel  265 

180.  Thought— Faculty  of— defined— Judgment ;  Apprehen- 

sion ;  Conception  is  a  Psychological  Judgment ; 
Conceiving  ;  Language  is  a  sign  of  Intuitions  ;  Ab- 
straction; Concept;  Common  Language  and  Com- 
mon Thought ;  Identity ;  Reasoning  defined  ;  Syl- 
logism ;  Recapitulation From  Mansel  266 

181.  Powers— Mental,  employed  in  acquiring  Knowledge- 

Discrimination;  Power  of  Detecting  Identity;  Power 
of  Retention From  Jevons  274 

182.  Identity  and  Difference— Laws  of.    (1)  Law  of  Identity; 

(2)  Law  of  Contradiction ;  (3)  Law  of  Duality. 

From  Jevons  277 

183.  Thought— First  Gradation  of,  is  the  Formation  of  Judg- 

ment—Proposition ;  Sentence  ;  Concept ;  Conceiv- 
ing ;  Reasoning  ;  Perception  ;  Regulative  Faculty, 
or  Faculty  of  Intuition  ;  Being ;  Existence  ;  Matter 
of  Thought ;  Analysis  ;  Abstraction  ;  Attention  ; 
Comparison;  Synthesis;  Subject;  Predicate;  Terms 
of  a  Proposition ;  Copula From  Day  279 

184.  Thought— Second  Gradation  of,  is  the  Formation  of 

Concept— Judgments ;  Forming  Concepts  ;  Terms  ; 
Concept  in  Comprehension  ;  Conception;  Faculty; 
Act ;  Product ;  Law  of  Identity  ;  Base  ;  Relative 
Cognition  ;  Concepts  differ  from  Judgments  ;  Con- 
cept not  Expressed  ;  Concept  implies  Judgments  ; 
Base  of  Concept;  Concepts  are  Products  of  Thought; 
Thought  aggregated  by  single  Words From  Day  288 

185.  Thought— Third  Gradation  of,  is  Reasoning— Reason- 

ing derived  from  Judgment ;  Reasoning  not  a  Con- 
clusion ;  Reasoning  defined ;  Ratiocination  ;  Dis- 
course ;  Discursive ;  Argumentation ;  Inference 
or  Illation  ;  Conclusion  ;  Syllogism  ;  Parts  of  Rea- 
soning ;  Antecedent ;  Consequent ;  Immediate  Rea- 
soning ;  Mediate  Reasoning —  -. From  Day  296 

186.  Reason— has  no  Relation  to  Body From  Grindon  301 

187.  Thinking  is  Conversation  of  Soul  with  itself. 

From  Mansel  301 


ANALYTICAL  TABLE  OF  CONTENTS.     XXV11 

(B)   On  the  Nature  of  Subject-Matter. 

SECTION  PAGE 

188.  Methods  of  Teaching— Teacher  to  discover,  must  know 

Mind  and  Nature  of  Subject-matter 302 

189.  Subject-matter—defined 302 

190.  Subject-matter— Material— Exists  outside  of  Mind 302 

191.  Subject-matter— Immaterial— Created  wholly  by  Mind.  302 

192.  Object  Teaching— Conception  of,  Analyzed 303 

193.  Object  Teaching— when  Valuable . .  304 

194.  Object  Teaching— when  Possible 304 

195.  Illustrative  Teaching— defined 304 

196.  Ideas— Succeed  each  other  according  to  Laws  of  Asso- 

ciation   305 

197.  Illustrations— defined,  by  Illustrations — defin- 
ed  From  Smith 

Analogy— defined From  Smith 

Analogy  and  Induction— Difference From  Fleming  305 

198.  Illustrations— Example  of From  Sterne  306 

199.  Illustrative  Teaching— Analogous  Extension  of  Mean- 

ing of  Words From  Jevons  309 

200.  Illustration— differs  from  Example 309 

201.  Illustrative  Teaching  is  Objective  Teaching 309 

202.  Illustrative  Teaching — Conception  of,  misunderstood 

for  Object  Teaching,  has  occasioned  abuse  of  the 
Expression 310 

203.  Mathematics— cannot  be  taught  by  Object  Teaching— 

only  Illustratively 310 

204.  Mathematics— Nature  of  Arithmetical  Numbers . 

From  Jevons 
Number — defined From  Davies  and  Peck  312 

205.  Mathematical  Judgments— on  Nature  of .  .From  Mansel  314 

206.  Mathematical  Judgments— on  Arithmetic,  Geometry. 

From  Eng.  Cycl.  324 

207.  Mathematical  Judgments— on  Numeration . 

From  Whewell  326 

208.  Object  Teaching— Branches  that  can  be  Taught  in  this 

way 327 

209.  Objects— when  their  Value    ceases  in   Teaching  and 

Learning 328 

210.  Object  Teaching— must  be  succeeded  by  Thought 329 


XXY111  ANALYTICAL  TABLE  OF  CONTENTS. 
(C)  On  Discovering  Methods  of  Teaching  Special  Subjects. 

SECTION  PAGE 

211.  System  of  Subject-matter  must   be   constructed   by 

Teacher— Principle  of  Adaptation  must  be  Discov- 
ered for  Method  of  Teaching 330 

212.  Addition— on  Discovering  the  Method  of  Teaching  it. . .  331 

(1)  On  the  Nature  of  the  Subject-matter 331 

(2)  On  the  Faculties  primarily  active  in  Learning  Ad- 

dition    332 

(3)  On  Inventing  the  Mode  of  Teaching  Addition 333 

213.  Mode  and  Manner  of  Teaching  Addition— Recapitu- 

lated   333 

214.  SCIENCE  OP  TEACHING— denned 334 

215.  ART  OF  TEACHING— denned 334 

216.  PROFESSION  OF  TEACHING— denned 334 

HI.  CONCLUDING  REFLECTIONS. 

217.  To  Teach— Qualifications  Requisite 335 

218.  Growth— Evil  effects  of  missing  Opportunities  for. 

From  Meikle John  335 

219.  Teacher— Should  be  a  Learner From  Arnold  336 

220.  Teacher— Value  of  Common-Sense From  Sidgwick  338 

221.  Teacher— Value  of  Common-Sense  for.. From  Whately  339 

222.  Teacher— Best  Talent  for,  is  Judging  Right  upon  Im- 

perfect Materials From  Stephen  344 

223.  Difference  between  Theory  and  Practice— of  Degree 

only,  not  of  Kind From  Mansel  344 

224.  Science  of  Human  Nature— Possible From  Mill  344 


APPENDIX  OF    QUOTATIONS. 


SECTION  PAGE 

225.  A.— On  METHOD. 

1.  From  Hedge 346 

2.  From  Coppee 347 

3.  From  Day „ 348 

4.  From  Fleming  350 

5.  From  Bain 356 

6.  FromWhewell. 357 

7.  From  Bowen 361 

8.  From  Day 368 

9.  From  Comte 373 

226.  B.— On  SYSTEM. 

1.  From  Fleming 376 

227.  C.— On  ANALYSIS. 

1.  From  Fleming 380 

228.  D.— On  SYNTHESIS. 

1.  From  Fleming 383 

229.  E.— On  DEFINITION. 

1.  From  Fleming 385 

2.  From  Mill 389 

230.  F.— On  ABSTRACTION. 

1.  From  Fleming 390 

231.  G.— On  GENERALIZATION. 

1.  From  Fleming...     392 

2.  From  Jevone 395 

232.  H.— On  CLASSIFICATION. 

1 .  From  Fleming 398 

2.  From  Jevons . . 401 

233.  I.— On  INDUCTION. 

1.  From  Smith 413 

2.  From  Day 415 


XXX  APPENDIX    OF    QUOTATIONS. 

SECTION  TAGZ 

3.  From  Fleming 416 

4.  From  Whewell 422 

5.  From  Eng.  Cyclop 423 

6.  From  Jevons 434 

7.  From  Mill 451 

234.  J.— On  INTERPRETATION. 

1.  From  Davies  and  Peck 473 

2.  From  Smith 477 

235.  K.— On  DEDUCTION, 

1.  From  Fleming 478 

2.  From  Day 480 

3.  From  Bowen 482 

4.  From  Hedge , 484 


INTRODUCTION. 

BY 

CHARLES  W.   BENNETT,   D.D. 


THE  subject  of  education  is  each  year  assum- 
ing growing  prominence.  It  cannot  be  justly 
charged  that  the  Eastern,  Middle,  and  Western 
States  of  the  American  Union  have  been  indiffer- 
ent to  the  claims  of  their  citizens  to  enjoy  op- 
portunities of  instruction  and  enlightenment. 
Nearly  all  of  them  have  made  generous  provi- 
sions for  primary  and  intermediate  instruction, 
and  in  some  have  been  elaborated  complete  sys- 
tems of  education  from  lowest  to  highest. 

Nor  has  the  question  of  Training  Schools  for 
teachers  been  neglected.  Good  general  educa- 
tion presupposes  good  schools,  and  good  schools 
presupposes  good  teachers  ;  hence  that  State 
which  fails  to  provide  for  good  teachers  exhibits 
a  plain  lack  of  practical  wisdom.  These  Nor- 
mal or  Training  Schools  have  been  subjected  to- 
severe  criticism,  both  as  to  the  scope  and  charac- 
ter of  their  work,  as  well  as  the  products  which 
they  have  yielded  to  the  State.  Many  able 
thinkers  have  believed  that  the  nature  and  prov- 
ince of  the  instruction  in  these  State  schools 
was  not  sufficiently  definitive  to  warrant  their 
independent  existence  and  exceptional  support  ; 


XXXIV  INTRODUCTION. 

that  the  Common  Schools,  Academies,  and  Sem- 
inaries of  the  State  were  doing  essentially  all 
which  was  accomplished  by  the  expensive  ma- 
chinery of  Normal  Schools  ;  that  the  conception 
of  the  use  and  design  of  Teachers7  Training 
Schools,  as  entertained  by  those  who  had  inaug- 
urated and  managed  them,  was  essentially  erro- 
neous ;  that  they  had  failed  to  elevate  teaching 
to  the  dignity,  honor,  and  emoluments  of  a  pro- 
fession ;  that  a  large  fraction  of  those  who  had 
been  thus  educated  chiefly  at  the  public  expense 
had  not  rendered  to  the  State  adequate  remun- 
eration in  superior  service  and  skilled  labor. 
Doubtless  some  of  the  writing  and  speaking  on 
this  subject  has  been  hypercritical  ;  since  the 
difficulties  of  the  educational  problem  have  not 
been  sufficiently  appreciated,  and  the  amount 
and  quality  of  the  hard  work  done  by  those  who 
have  had  charge  of  these  Training  Schools  have 
not  been  properly  recognized.  Nevertheless, 
that  the  expectations  of  the  best  friends  of  edu- 
cation have  not  been  fully  satisfied  must  be 
frankly  acknowledged.  Too  much  time  and  en- 
ergy have  been  consumed  in  the  mere  prelimin- 
aries to  strictly  Training  Schools.  The  require- 
ments for  admission  have  been  too  low.  The 
three  great  departments  of  Psychology,  History 
of  Pedagogics,  and  Methodology  and  Training, 
which  should  occupy  by  far  the  largest  portion 
of  the  course  of  study,  have  been  in  too  many 
instances  but  meagrely  examined,  and  in  most 
of  these  schools  the  historical  examination  has 
scarcely  been  touched  upon  at  all. 


ItfTKODUCTION.  XXXV 

We,  therefore,  welcome  the  present  work  of 
Dr.  Hoose  as  a  promise  that  a  better  day  for 
Normal  School  Training  is  dawning.  It  shows 
that  at  least  one  Chief  in  these  Schools  is  fully 
awake  to  the  necessity  of  careful  and  exact 
thinking  on  one  of  the  few  subjects  of  study 
which  legitimately  belong  to  Training  Schools. 
The  importance  of  the  branch  of  education  here 
treated  can  hardly  be  over-emphasized.  Lack 
of  clearness  here  brings  obscurity  and  partial 
failure  into  the  whole  career  of  the  teacher.  He 
may,  by  long  experimentation  with  mind,  cor- 
rect some  mistakes  ;  but  unless  the  principle 
which  underlies  Method  is  fully  understood  in 
the  outset,  it  is  difficult  to  compute  the  mischief 
which  may  ensue. 

The  work  which  is  here  presented  professes  to 
reveal  and  discuss  this  principle.  As  stated  in 
his  preface,  during  the  ten  years  of  his  supervi- 
sion of  one  of  the  largest  Training  Schools  of 
New  York,  the  author  has  been  continually  study- 
ing, and  yearly  developing  this  subject  before  the 
classes  which  have  been  under  his  tuition.  Like 
most  valuable  products  it  has,  therefore,  been  a 
growth  from  the  experience  and  close  observa- 
tion of  an  eminently  practical  teacher.  This 
should  greatly  enhance  its  value.  In  the  direct- 
ness, brevity,  and  pertinence  of  statement  and  il- 
lustration, the  author  seems  to  have  the  wants 
of  his  classes  ever  distinctly  before  him.  Evi- 
dently he  is  no  recluse  thinker,  but  a  busy  man 
among  busy  men  and  women  who  need  his  help, 
and  whom  he  wants  to  help. 


XXXY1  INTRODUCTION. 

The  extended  quotations  from  so  many  emi- 
nent thinkers  and  educators  may,  in  the  opinion 
of  some,  smack  a  little  of  pedantry.  But  since 
one  great  object  of  such  a  work  is  to  stimulate 
to  further  research,  as  well  as  to  instruct  the  un- 
initiated, these  references  to  and  quotations 
from  the  works  of  philosophic  thinkers  must  be 
regarded  not  only  pertinent,  but  invaluable. 
Moreover,  the  assumption  of  originality  may  be 
cheap  with  those  of  slender  information,  but  the 
real  student  becomes  quite  content  at  times  to 
sit  at  the  feet  of  those  giants  who  have  wrestled 
with  the  hard  problems  of  education,  and  endeav- 
or to  reduce  their  thoughts  to  practical  and  effi- 
cient uses.  He  usually  does  most  for  his  pupils 
and  readers  who  opens  up  to  them  the  literature 
of  his  subject,  and  directs  them  to  the  sources  of 
his  own  inspiration  and  quickening.  The  teacher 
in  Training  Schools  especially  must  ever  consider 
that  he  is  dealing  with  minds  of  greater  or  less 
maturity,  who  are,  with  himself,  desirous  to  go 
to  the  fountain-heads  of  knowledge  and  truth, 
and  there  drink  for  themselves.  While  this 
course  of  procedure  may  prove  terribly  iconoclas- 
tic to  those  who  may  be  worshipping  the  false 
idol  of  originality,  it  will  always  be  most  help- 
ful to  the  real  lover  of  truth,  and  become  most 
beneficent  to  our  fellow-workers. 

It  is  highly  probable  that  some  positions  of  the 
author  will  not  pass  unchallenged.  Some  read- 
ers may  be  inclined  to  believe  that  his  boldness 
sometimes  verges  on  rashness,  and  that  in  some 
points  he  has  not  fully  established  what  he 


INTRODUCTION.  XXXYli 

claims  :  but  in  all  the  work  there  breathes  the 
spirit  of  honest  conviction  ;  and  honest  thinking 
cannot  long  remain  wrong  thinking  after  the 
wrong  has  been  pointed  out.  If  by  frank  and 
generous  criticism  it  shall  be  shown  that  the  au- 
thor has  inadvertently  been  led  to  make  any  mis- 
statements  of  fact  or  principle,  these  corrections 
will  probably  be  thankfully  received,  and  can  be 
easily  incorporated  into  the  text  of  some  future 
edition. 

The  subject  here  presented  by  Dr.  Hoose  is 
specially  worthy  of  investigation  and  attention 
on  the  part  of  the  directors  of  Training  Schools  ; 
indeed,  none  are  of  greater  value.  Hence  we 
must  believe  that  this  work  will  be  cordially  wel- 
comed by  the  teachers  of  Normal  Schools,  by 
the  graduating  classes  of  these  schools,  and  by 
all  thorough  teachers,  as  supplying  a  long-felt 
need. 

CHAS.  W.  BENNETT. 
SYRACUSE  UNIVERSITY,  January  1,  1879. 


PAET   FIEST. 

§§  1-35. 

INTRODUCTORY  DISCUSSION. 


I.  ON  PEDAGOGICS,  .        .      " .        .    g  §  1-3. 

II.  ON  EDUCATION,  .  .  .  §  §  4-19. 

III.  ON  TEACHING,  .  .  .  §  §  20-30. 

IV.  ON  AUTHORITIES,  .  .  .  §  §  31-34. 

V.  RECAPITULATION,  ....         §  35. 


U1TIVEESIT7 


ON  PEDAGOGICS. 

1.  "By  Pedagogics  we  mean  the  science  of 
the  realization  of  the  human  rational  potentiality 
into  actuality.  In  the  human  mind  lie  certain 
capabilities  which  do  not  manifest  themselves 
unless  drawn  out  by  external  influence  or  an 
inherent  principle  of  development.  Although 
there  be  no  development  of  these  faculties,  they 
may  still  exist,  but  are  not  manifest.  They  re- 
main in  a  dormant  or  latent  state,  they  exist  as 
possibilities,  or  in  potentia.  By  an  educating 
or  developing  influence  these  latent  capabilities 
become  manifest,  and  from  the  state  of  potenti- 
ality pass  over  to  the  state  of  actuality.  To  use 
an  illustration,  we  may  say  that  the  seed  makes 
the  growth  of  the  plant  possible  :  it  contains  the 
possibility  of  the  plant.  Hence,  to  express  the 
same  thought  in  a  different  way  :  The  seed  is  the 
potentiality  of  the  plant  ;  sun  and  soil  will  trans- 
form this  potentiality  into  actuality,  the  plant  it- 
self. All  actual,  finite  existence  must  have  passed 
through  the  stage  of  potential  existence.  Peda- 
gogics is  the  science  of  the  transition  of  man 
from  his  natural  potentiality  to  actuality." 
(Proceedings  of  the  National  Educational  Asso- 


4  ON   PEDAGOGICS. 

elation,  1874,  p.  246.  Paper  by  Prof.  Louis 
Soldan.) 

2.  "  Pedagogics  as  a  science  must  (1)  unfold 
the  general  idea  of  Education  ;  (2)  must  exhibit 
the  particular  phases  into  which  the  general  work 
of  Education  divides  itself,  and  (3)  must  describe 
the  particular  standpoint  upon  which  the  general 
idea  realizes  itself,  or  should  become  real  in  its 
special  processes  at  any  particular  time. 

It  busies  itself  with  developing  a  priori  the  idea 
of  Education  in  the  universality  and  necessity  of 
that  idea.  .  .  .  Pedagogics  as  an  art  is  the 
concrete  individualizing  of  this  abstract  idea  in 
any  given  case.  .  .  .  The  idea  of  Pedagog- 
ics in  general  must  distinguish,  (1)  The  nature 
of  Education  in  general ;  (2)  Its  form  ;  (3)  Its 
limits. '  '  (Rosenkranz,  Pedagogics  as  a  System, 
pp.  7-9,  ed.  1873.  Translated  by  Anna  C. 
Brackett.) 

3.  "  Pedagogics  is  the  science  and  art  of  so 
developing,  by  means  of  conscious  influence  on 
the  physical,   intellectual,  and  moral   powers  of 
man,  the  ideas  of  truth,  freedom,  and  love,  that 
lie  at  the  foundation  of  his  God-derived  nature, 
that  he  can  meet  spontaneously,   and  indepen- 
dently, his  human  responsibilities. ' '     (Schmidt, 
Geschichte  der  Erziehung,  p.  1,  quoted  by  Dr. 
C.  W.  Bennett  in  History  of  the  Philosophy  of 
Pedagogies,  p.  2,  a  paper  published  by  E.  Stei- 
ger,  New  York,  1877.) 


II. 

ON   EDUCATION. 

4.  Man  lives  upon  the  earth  as  a  member  of  a 
family,  as  a  member  of  society,  as  a  member  of 
the  state,  and  as  an  individual.     These  ethical  re- 
lations and  the  natural  surroundings  constitute 
the  environment  which  encircle  and  mould  him. 
Whatever  influence  this  environment  has  upon 
his  native  capacities  and    faculties  to  occasion 
them  to  grow  into  powers,  or  habits,  is  called 
Education. 

5.  "  We  are  born  weak,  we  have  need  of  help  ; 
we  are  born  destitute  of  every  thing,  we  stand 
in  need  of  assistance  ;  we  are  born  stupid,  we 
have  need  of  understanding.     All  that  we  are  not 
possessed  of  at  our  birth,  and  which  we  require 
when  grown  up,  is  bestowed  on  us  by  education. 
This    education  we    receive   from  nature,   from 
men,  or  from  circumstances.     The  constitutional 
exertion  of  our  organs  and  faculties  is  the  educa- 
tion of  nature  ;  the  uses  we  are  taught  to  make 
of  that  exertion  constitute  the  education  given 
us  by  men  ;  and  in  the  acquisitions  made  by  our 
own  experience,  on  the  objects  that  surround  us, 
consists  our  education  from  circumstances.     We 
are  formed,  therefore,  by  three  kinds  of  masters* 


6  02^   EDUCATION. 

The  pupil,  in  whom  the  effects  of  their  different 
lessons  are  contradictory,  is  badly  educated,  and 
can  never  be  consistent  with  himself.  He,  in 
whom  they  are  perfectly  consonant,  and  always 
tend  to  the  same  point,  hath  only  attained  the 
end  of  a  complete  education.  His  life  and  ac- 
tions demonstrate  this,  and  that  he  alone  is  well 
brought  up.  Of  these  three  different  kinds  of 
education,  that  of  nature  depends  not  on  our- 
selves ;  and  but  in  a  certain  degree  that  of  cir- 
cumstances :  the  third,  which  belongs  to  men,  is 
that  only  we  have  in  our  power  :  and  even  of 
this  we  are  masters  only  in  imagination  ;  for  who 
can  flatter  himself  he  will  be  able  entirely  to  gov- 
ern the  discourse  and  actions  of  those  who  are 
about  a  child  ?"  (Rousseau,  Emilius  and  So- 
phia, vol.  1,  pp.  4,  5.  London,  4  vols.,  1783.) 
6.  "  Education  is  the  influencing  of  man  by 
man,  and  it  has  for  its  end  to  lead  him  to  actual- 
ize himself  through  his  own  efforts. 
It  is  the  nature  of  education  only  to  assist  in  the 
producing  of  that  which  the  subject  would  strive 
most  earnestly  to  develop  for  himself  if  he  had  a 
clear  idea  of  himself.  .  .  .  Man,  therefore, 
is  the  only  fit  subject  for  education.  We  often 
speak,  it  is  true,  of  the  education  of  plants  and 
animals  ;  but  even  when  we  do  so,  we  apply, 
unconsciously  perhaps,  other  expressions,  as  *  rais- 
ing '  and  '  training, '  in  order  to  distinguish  these. 
The  general  form  of  Education  is  determined  by 
the  nature  of  the  mind,  that  it  really  is  nothing 
but  what  it  makes  itself  to  be.  The  mind  is  (1) 
immediate  (or  potential),  but  (2)  it  must 


OX   EDUCATION.  7 

estrange  itself  from  itself  as  it  were,  so  that  it 
may  place  itself  over  against  itself  as  a  special 
object  of  attention  ;  (3)  this  estrangement  is  fin- 
ally removed  through  a  further  acquaintance 
with  the  object.  .  .  .  Education  cannot 
create  :  it  can  only  help  to  develop  to  reality  the 
previously  existent  possibility  ;  it  can  only  help 
to  bring  forth  to  light  the  hidden  life. 
Education  seeks  to  transform  every  particular 
condition  so  that  it  shall  no  longer  seem  strange 
to  the  mind  or  in  any  wise  foreign  to  its  own 
nature.  This  identity  of  consciousness,  and  the 
special  character  of  any  thing  done  or  endured  by 
it,  we  call  Habit  (habitual  conduct  or  behavior). 
It  conditions  formally  all  progress  ;  for  that 
which  is  not  yet  become  habit,  but  which  we 
perform  with  design  and  an  exercise  of  our  will, 
is  not  yet  a  part  of  ourselves.  .  .  .  The 
limits  of  Education  are  found  in  the  idea  of  its 
nature,  which  is  to  fashion  the  individual  into 
theoretical  and  practical  rationality."  (Rosen- 
kranz,  Pedagogics  as  a  System,  pp.  7—23,  ed. 
1872,  St.  Louis.  Translated  by  Anna  C.  Brac- 
kett.) 

7.  "  Education  differs  from  information  or 
knowledge.  The  latter  is  of  a  special  character, 
the  purport  of  which  is  to  fit  a  man  for  bringing 
about  certain  definite  results  by  the  immediate 
operation  of  that  knowledge  which  he  possesses. 
We  talk,  indeed,  of  the  education  of  a  lawyer, 
a  doctor,  and  a  clergyman — of  an  engineer,  a 
soldier,  or  a  sailor  ;  generally  meaning  by  it  the 
information  or  knowledge  which  he  has  acquired 


ON    EDUCATION. 

for  the  immediate  exercise  of  his  vocation.  But 
law,  medicine,  divinity,  mechanics,  strategics, 
and  navigation,  are  not  education.  A  man  may 
possess  any  one  of  them  and  be  well-nigh  illite- 
rate, though  of  course  some  can  more  possibly 
co-exist  with  want  of  education  than  others. 
One  can  conceive  that  a  man  may  have  a  pro- 
found practical  acquaintance  with  law,  and  be  an 
uneducated  person.  Again,  to  quote  an  in- 
stance, the  first  Duke  of  Marlborough  was  one 
of  the  most  skilful  generals  ever  known,  but  he 
could  not  spell,  and  hardly  write.  Some  men 
who  have  had  the  most  marvellous  aptitude  and 
quickness  in  mechanical  science,  have  been  un- 
able, from  sheer  ignorance,  to  sustain  a  common 
conversation.  Education,  on  the  other  hand, 
deals  with  formalities.  It  does  not  so  much 
aim  at  setting  the  mind  right  on  particular  points, 
as  on  getting  the  mind  into  the  way  of  being 
right.  It  does  not  deal  with  matter,  but  with 
method.  It  purposes  to  train  the  thinking  pow- 
ers of  man,  not  to  fill  the  mind  with  facts. 
Hence,  were  it  perfect,  it  would  cultivate  the  in- 
telligence so  largely  as  to  render  easy  the  acqui- 
sition of  any  knowledge.  It  deals,  in  short, 
cither  directly  or  indirectly,  with  logical  order 
and  the  reasoning  powers.  That  it  falls  short  of 
effecting  what  it  purposes,  is  due  to  defects 
in  its  system,  to  defects  in  man's  mind,  to  de- 
fects in  this  or  that  man's  mind.  As,  however, 
its  operation  is  not  immediate,  but  only  indi- 
rect, its  best  methods  are  frequently  cavilled  at 
!as  useless.  It  may  teach  logical  method  of 


ON   EDUCATION.  9 

thinking  and  reasoning.  This,  however,  is  gen- 
erally too  abstract  for  most  minds,  except  they 
be  more  or  less  matured,  and  more  or  less  in- 
formed on  some  one  or  two  subjects.  In  place 
of  this,  then,  it  teaches  ordinarily  something, 
which  is  as  exact  an  illustration  of  logical 
method  as  can  be,  and  which,  being  unfailing  in 
its  inferences,  trains  the  mind  in  method,  and 
often  stores  it  with  facts.  In  a  greater  or  less 
degree,  but  in  some  degree  at  least,  this  inculca- 
tion of  an  abstract  method  is  necessary  for  any 
kind  of  education,  and  even,  except  it  be  a  mere 
knack,  for  information."  (Rogers,  Education 
in  Oxford ,  pp.  1—3.  London,  1861.) 

8.  In  the  following  quotation  the  extension 
of  the  term  education  is  limited  substantially  to 
the  work  of  the  teacher.  This  limitation  is  un- 
usual, and  the  advantages  gained  by  it  are  hard- 
ly evident :  ' l  First,  let  me  quote  the  definition 
(of  Education)  embodied  in  the  ideal  of  the  foun- 
ders of  the  Prussian  National  System.  It  is 
given  shortly  as  *  the  harmonious  and  equable 
evolution  of  the  human  powers  ;'  at  more  length, 
in  the  words  of  Stein,  '  by  a  method  based  on 
the  nature  of  the  mind,  every  power  of  the  soul 
to  be  unfolded,  every  crude  principle  of  life 
stirred  up  and  nourished,  all  one-sided  culture 
avoided,  and  the  impulses  on  which  the  strength 
and  worth  of  men  rest,  carefully  attended  to. ' 
(Donaldson's  Lectures  on  Education,  p.  38.) 
This  definition,  which  is  pointed  against  narrowT- 
ness  generally,  may  have  had  special  reference  to 
the  many  omissions  in  the  schooling  of  the  fore- 


10  ON   EDUCATION. 

gone  times  :  the  leaving  out  of  such  things  as 
bodily  or  muscular  training  ;  training  in  the 
senses  or  observation  ;  training  in  art  or  refine- 
ment. It  farther  insinuates  that  hitherto  the 
professed  teacher  may  not  have  done  much  even 
for  the  intellect,  for  the  higher  moral  training, 
nor  for  the  training  with  a  view  to  happiness  or 
enjoyment.  .  . 

"  In  the  very  remarkable  article  on  education 
contributed  by  James  Mill  to  the  Encyclopaedia 
Britannica,  the  end  of  education  is  stated  to  be 
*  to  render  the  individual,  as  much  as  possible, 
an  instrument  of  happiness,  first  to  himself,  and 
next  to  other  beings. '  This,  however,  should  be 
given  as  an  amended  answer  to  the  first  question 
of  the  Westminster  Catechism — '  What  is  the 
,  chief  end  of  man  ? '  The  utmost  that  we  could 
\expect  of  the  educator,  who  is  not  everybody, 
is  to  contribute  his  part  to  the  promotion  of  hu- 
man happiness  in  the  order  stated.  No  doubt 
the  definition  goes  more  completely  to  the  root 
of  the  matter  than  the  German  formula.  It  does 
not  trouble  itself  with  the  harmony,  the  many- 
sidedness,  the  wholeness,  of  the  individual  de- 
velopment ;  it  would  admit  these  just  as  might 
be  requisite  for  securing  the  final  end. 

"  James  Mill  is  not  singular  in  his  over -grasp- 
ing view  of  the  subject.  The  most  usual  sub- 
division of  Education  is  into  Physical,  Intellect- 
ual, Moral,  Religious,  Technical.  Now  when  we 
inquire  into  the  meaning  of  Physical  Education, 
we  find  it  to  mean  the  rearing  of  a  healthy  hu- 
man being,  by  all  the  arts  and  devices  of  nursing 


ON   EDUCATION.  11 

feeding,  clothing,  and  general  regimen.  Mill  in- 
cludes this  subject  in  his  article,  and  Mr.  Her- 
bert Spencer  devotes  a  very  interesting  chapter  to 
it  in  his  work  on  Education.  It  seems  to  me, 
however,  that  this  department  may  be  kept  quite 
separate,  important  though  it  be.  It  does  not 
at  all  depend  upon  the  principles  and  considera- 
tions that  the  educator,  properly  so  called,  has  in 
view  in  the  carrying  on  of  his  work.  The  dis- 
cussion of  the  subject  does  not  in  any  way  help 
us  in  educational  matters,  as  most  commonly  un- 
derstood ;  nor  does  it  derive  any  illumination 
from  being  placed  side  by  side  with  the  arts  of 
the  recognized  teacher.  The  fact  of  bodily 
health  or  vigor  is  a  leading  postulate  in  bodily 
or  mental  training,  but  the  trainer  does  not  take 
upon  himself  to  lay  down  the  rules  of  hygiene. 

"  The  inadvertence,  for  so  I  regard  it,  of 
coupling  the  Art  of  Health  with  Education  is  eas- 
ily disposed  of,  and  does  not  land  us  in  any  ard- 
uous controversies.  Very  different  is  another 
aspect  of  these  definitions:  that  wherein  the  end 
of  Education  is  propounded  as  the  promotion  of 
human  happiness,  human  virtue,  human  perfec- 
tion. Probably  the  qualification  will  at  once  be 
conceded,  that  Education  is  but  one  of  the  means, 
a  single  contributing  agency  to  the  all-including 
end.  Nevertheless,  the  openings  for  difference 
of  opinion  as  to  what  constitutes  happiness,  vir- 
tue or  perfection,  are  very  wide.  Moreover,  the 
discussion  has  its  proper  place  in  Ethics  and  in 
Theology,  and  if  brought  into  the  field  of  Educa- 
tion, should  be  received  under  protest. 


12  Otf  EDUCATION. 

"  Before  entering  upon  the  consideration  of 
this  difficulty,  the  greatest  of  all,  I  will  advert  to 
some  of  the  other  views  of  education  that  seem 
to  err  on  the  side  of  taking  in  too  much.  Here, 
I  may  quote  from  the  younger  Mill,  who,  like 
his  father,  and  unlike  the  generality  of  theorists, 
starts  more  scientifieo  with  a  definition.  Edu- 
cation, according  to  him,  '  includes  whatever  we 
do  for  ourselves,  and  whatever  is  done  for  us  by 
others,  for  the  express  purpose  of  bringing  us 
nearer  to  the  perfection  of  our  nature  ;  in  its 
largest  acceptation,  it  comprehends  even  the  in- 
direct effects  produced  on  character  and  on  the 
human  faculties  by  things  of  which  the  direct 
purposes  are  different  ;  by  laws,  by  forms  of 
government,  by  the  industrial  arts,  by  modes  of 
social  life  ;  nay  even  by  physical  facts  not  depen- 
dent on  the  human  will  ;  by  climate,  soil,  and 
local  position.'  He  admits,  however,  that  this 
is  a  very  wide  view  of  the  subject,  and  for  his 
own  immediate  purpose  advances  a  narrower 
view,  namely,  '  the  culture  which  each  genera- 
tion purposely  gives  to  those  who  are  to  be  its 
successors,  in  order  to  qualify  them  for  at  least 
keeping  up,  and  if  possible  for  raising,  the  im- 
provement which  has  been  attained. '  (Inaugu- 
ral Address  at  St.  Andrew's,  p.  4.) 

"  Besides  involving  the  dispute  as  to  what 
constitutes  4  perfection, '  the  first  and  larger  state- 
ment is,  I  think,  too  wide  for  the  most  compre- 
hensive Philosophy  of  Education.  The  influ- 
ences exerted  on  the  human  character  by  climate 
and  geographical  position,  by  arts,  laws,  govern- 


ON   EDUCATION.  13 

ment  and  modes  of  social  life,  constitute  a  very 
interesting  department  of  Sociology,  and  have 
their  place  there  and  nowhere  else.  What  we 
do  for  ourselves,  and  what  others  do  for  us,  to 
bring  us  nearer  to  the  perfection  of  our  nature, 
may  be  education  in  a  precise  sense  of  the  word, 
and  it  may  not.  I  do  not  see  the  propriety  of 
including  under  the  subject  the  direct  operation 
of  rewards  and  punishments.  No  doubt  we  do 
something  to  educate  ourselves,  and  society  does 
something  to  educate  us,  in  a  sufficiently  proper 
acceptation  of  the  word  ;  but  the  ordinary  influ- 
ence of  society,  in  the  dispensing  of  punishment 
and  reward,  is  not  the  essential  fact  of  Educa- 
tion, as  I  propose  to  regard  it,  although  an  ad- 
junct to  some  of  its  legitimate  functions. 

"  Mill's  narrow  expression  of  the  scope  of  the 
subject  is  not  exactly  erroneous  ;  the  moulding 
of  each  generation  by  the  one  preceding  is  not 
improperly  described  as  an  Education.  It  is, 
however,  grandiose  rather  than  scientific.  Noth- 
ing is  to  be  got  out  of  it.  It  does  not  give  the 
lead  to  the  subsequent  exposition. 

"  I  find  in  the  article  '  Education,'  in  Cham- 
bers's  Encyclopaedia,  a  definition  to  the  following 
effect  :  i  In  the  widest  sense  of  the  word  a  man 
is  educated,  either  for  good  or  for  evil,  by 
every  thing  that  he  experiences  from  the  cradle 
to  the  grave  [say,  rather,  "  formed, "  "  made," 
"influenced"].  But  in  the  more  limited  and 
usual  sense,  the  term  Education  is  confined  to 
the  efforts  made,  of  set  purpose,  to  train  men  in 
a  particular  way — the  efforts  of  the  grown-up 


14  ON    EDUCATION. 

part  of  the  community  to  inform  the  intellect 
and  mould  the  character  of  the  young  [rather  too 
much  stress  on  the  fact  of  influence  from  with- 
out] ;  and  more  especially  to  the  labours  of  pro- 
fessional educators  or  schoolmasters. '  The  con- 
cluding clause  is  the  nearest  to  the  point — the 
arts  and  methods  employed  by  the  schoolmas- 
ters ;  for,  although  he  is  not  alone  in  the  work 
that  he  is  expressly  devoted  to,  yet  he  it  is  that 
typifies  the  process  in  its  greatest  singleness  and 
purity.  If  by  any  investigations,  inventions  or 
discussions,  we  can  improve  his  art  to  the  ideal 
pitch,  we  shall  have  done  nearly  all  that  can  be 
required  of  a  science  and  art  of  Education. " 
(Bain,  Education  as  a  Science,  Art.  I.,  in  Mind, 
pp.  1-4,  No.  5,  January,  1877.) 

9.  "  The  true  view  of  education  is  to  regard 
it  as  a  course  of  training.  The  youth  in  a  gymna- 
sium practises  upon  the  horizontal  bar,  in  order 
to  develop  his  muscular  powers  generally  ;  he 
does  not  intend  to  go  on  posturing  upon  hori- 
zontal bars  all  through  'life.  School  is  a  place 
where  the  mental  fibres  are  to  be  exercised, 
trained,  expanded,  developed,  and  strength- 
ened. .  .  .  It  is  the  very  purpose  of  a  lib- 
eral education,  as  it  is  correctly  called,  to  de- 
velop and  train  the  plastic  fibres  of  the  youthful 
brain,  so  as  to  prevent  them  taking  too  early  a 
definite  i  set/  which  will  afterwards  narrow  and 
restrict  the  range  of  acquisition  and  judgment. 
I  will  even  go  so  far  as  to  say  that  it  is  hardly 
desirable  for  the  actual  things  taught  at  school 
to  stay  in  the  mind  for  life.  The  source  of 


Otf   EDUCATION.  15 

error  is  the  failure  to  distinguish  between  the 
form  and  the  matter  of  knowledge,  between  the 
facts  themselves  and  the  manner  in  which  the 
mental  powers  deal  with  facts.  .  .  .  It  is 
the  purpose  of  education  so  to  exercise  the  fac- 
ulties of  mind  that  the  infinitely  various  experi- 
ence of  after-life  may  be  observed  and  reasoned 
upon  to  the  best  effect/'  (Jevons,  in  Mind, 
pp.  197-207,  No.  VI.,  April,  1877.)  (Rein- 
serted under  "  Memory  and  Cram,"  §  172.) 

10.  "  Educit  obstetrix,  educat  nutrix,  insti- 
tuit     pedagogus,     docet    magister. "       (Varro. 
See  also  An.  and  Stjd  Lat.  Lex.,  unabridged.) 

11.  "  TRAINING  (Fr.  Cramer)  is  development 
by  instruction,  exercise,  and   discipline,  and    is 
applicable  to  the  whole  nature  of    a  man,   or, 
specifically,  to  the  faculties  which  he  possesses. 
It  denotes  no  more  than  a  process  of  purposed 
habituation,  and  is  equally  applicable  to  the  phy- 
sical and  mental  powers,  so  that  it  may  include 
both  at  the  same  time."     (Smith,  Syn.  Discri- 
minated,   Art.     Education,    ed.     1878.)     This 
sense  of  training  is  the  ordinary  meaning  now 
attached  to  education. 

12.  "A  thorough    and  complete   education 
ought  to  preserve  and  increase  the  pupil's  bodily 
health  and  strength  ;  give  him  command  of  his 
own  muscular  and  mental  powers  ;  increase  his 
quickness  in  perceiving  through  his  five  senses, 
and  quicken  his  mental  perception  ;  form  in  him 
the  habit  of    prompt  and    accurate  judgment  ; 
lead  to  delicacy  and  depth  in  every  right  feel- 
ing ;  and  make  him  inflexible  in  his  conscien- 


OT  THE 

[UIUYIESITY] 


16  ON   EDUCATION. 

tious  and  steadfast  devotion  to  all  his  duties. 
In  other  words,  an  integral  education  must  in- 
clude at  least  these  four  branches  : — gymnastics, 
or  care  of  the  body  ;  noetics,  or  training  of  the 
mind  ;  aesthetics,  or  cultivation  of  the  tastes  ; 
and  ethics,  which  shall  include  religion  as  well 
as  duty.  And  in  every  part  of  each  branch  of 
education,  there  will  be  a  double  end  in  view, 
namely,  the  increase  of  knowledge,  and  the  in- 
crease of  skill.  Each  study  may  be  made  the 
object  of  thought,  or  the  object  of  action  ;  in 
the  one  case  it  is  pursued  as  a  science  ;  in  the 
other  case  as  an  art."  (Thomas  Hill,  The  True 
Order  of  Studies,  pp.  7,  8,  ed.  1876.) 

13.  "  The  conclusions  of  the  honest  and  in- 
telligent inquirer  after  the  truth  in  this  matter, 
will  be  something  like  the  following  : — That  edu- 
cation (from  e  and  duco,  to  lead  forth)  is  devel- 
opment ;  that  it  is  not  instruction  merely — 
knowledge,  facts,  rules — communicated  by  the 
teacher,  but  it  is  discipline,  it  is  a  waking  up 
of  the  mind,  a  growth  of  the  mind, — growth  by 
a  healthy  assimilation  of  wholesome  aliment.  It 
is  an  inspiring  of  the  mind  with  a  thirst  for 
knowledge,  growth,  enlargement, — and  then  a  dis- 
ciplining of  its  powers  so  far  that  it  can  go  on  to 
educate  itself.  It  is  the  arousing  of  the  child's 
mind  to  think,  without  thinking  for  it  ;  it  is  the 
awakening  of  its  powers  to  observe,  to  remem- 
ber, to  reflect,  to  combine.  It  is  not  a  cultiva- 
tion of  the  memory  to  the  neglect  of  every  thing 
else  ;  but  it  is  a  calling  forth  of  all  the  faculties 
into  harmonious  action.  If  to  possess  facts  sim- 


ON   EDUCATION.  17 

ply  is  education,  then  an  encyclopaedia  is  better 
educated  than  a  man."  (Page,  Theory  and 
Practice  of  Teaching,  p.  70,  ed.  1853.) 

14.  "  Suppose  it  were  perfectly  certain  that 
the  life  and  fortune  of  every  one  of  us  would, 
one  day  or  other,  depend  upon  his  winning  or 
losing  a  game  at  chess.  Don't  you  think  that 
we  should  all  consider  it  to  be  a  primary  duty  to 
learn  at  least  the  names  and  the  moves  of  the 
pieces  ;  to  have  a  notion  of  a  gambit,  and  a  keen 
eye  for  all  the  means  of  giving  and  getting  out 
of  check  ?  Do  you  not  think  that  we  should 
look  with  disapprobation  amounting  to  scorn, 
upon  the  father  who  allowed  his  son,  or  the 
state  which  allowed  its  members,  to  grow  up 
without  knowing  a  pawn  from  a  knight  ? 

'  *  Yet  it  is  a  very  plain  and  elementary  truth, 
that  the  life,  the  fortune,  and  the  happiness  of 
eyery  one  of  us,  and,  more  or  less,  of  those  who 
are  connected  with  us,  do  depend  upon  our 
knowing  something  of  the  rules  of  a  game  infin- 
itely more  difficult  and  complicated  than  chess. 
It  is  a  game  which  has  been  played  for  untold 
ages,  every  man  and  woman  of  us  being  one  of 
the  two  players  in  a  game  of  his  or  her  own. 
The  chess-board  is  the  world,  the  pieces  are  the 
phenomena  of  the  universe,  the  rules  of  the 
game  are  what  we  call  the  laws  of  Nature.  The 
player  on  the  other  side  is  hidden  from  us. 
We  know  that  his  play  is  always  fair,  just,  and 
patient.  But  also  we  know,  to  our  cost,  that 
he  never  overlooks  a  mistake,  or  makes  the  small- 
est aMowance  for  ignorance.  To  the  man  who 


18  ON    EDUCATION. 

plays  well  the  highest  stakes  are  paid,  with  that 
sort  of  overflowing  generosity  with  which  the 
strong  shows  delight  in  strength.  And  one  who 
plays  ill  is  checkmated — without  haste,  but  with- 
out remorse. 

"  My  metaphor  will  remind  some  of  you  of 
the  famous  picture  in  which  Retzsch  has  de- 
picted Satan  playing  at  chess  with  man  for  his 
soul.  Substitute  for  the  mocking  fiend  in  that 
picture,  a  calm,  strong  angel  who  is  playing  for 
love,  as  we  say,  and  would  rather  lose  than  win 
— and  I  should  accept  it  as  an  image  of  human 
life. 

"  Well,  what  I  mean  by  Education  is  learning 
the  rules  of  this  mighty  game.  In  other  words, 
education  is  the  instruction  of  the  intellect  in  the 
laws  of  Nature,  under  which  name  I  include  not 
merely  things  and  their  forces,  but  men  and 
their  ways  ;  and  the  fashioning  of  the  affections 
and  of  the  will  into  an  earnest  and  loving  desire 
to  move  in  harmony  with  those  laws.  For  me, 
education  means  neither  more  nor  less  than  this. 
Any  thing  which  professes  to  call  itself  education 
must  be  tried  by  this  standard,  and  if  it  fails  to 
stand  the  test,  I  will  not  call  it  education,  what- 
ever may  be  the  force  of  authority,  or  of  num- 
bers, upon  the  other  side. 

"  It  is  important  to  remember  that,  in  strict- 
ness, there  is  no  such  thing  as  an  uneducated 
man.  Take  an  extreme  case.  Suppose  that  an 
adult  man,  in  the  full  vigour  of  his  faculties, 
could  be  suddenly  placed  in  the  world,  as  Adam 
is  said  to  have  been,  and  then  left  to  do  as  he 


ON   EDUCATION.  19 

best  might.  How  long  would  he  be  left  unedu- 
cated ?  Not  five  minutes.  Nature  would  begin 
to  teach  him,  through  the  eyer  the  ear,  the 
touch,  the  properties  of  objects.  Pain  and 
pleasure  would  be  at  his  elbow  telling  him  to  do 
this  and  avoid  that  ;  and  by  slow  degrees  the 
man  would  receive  an  education,  which,  if  nar- 
row, would  be  thorough,  real,  and  adequate  to 
his  circumstances,  though  there  would  be  no  ex- 
tras and  very  few  accomplishments. 
The  great  mass  of  mankind  are  the  *  Poll, '  who 
pick  up  just  enough  to  get  through  without  much 
discredit.  Those  who  won't  learn  at  all  are 
plucked  ;  and  then  you  can't  come  up  again. 
Nature's  pluck  means  extermination. 
Nature's  discipline  is  not  even  a  word  and  a 
blow,  and  the  blow  first  ;  but  the  blow  without 
the  word.  It  is  left  to  you  to  find  out  why  your 
ears  are  boxed. ' '  (Huxley,  Lay  Sermons,  pp. 
31-34,  ed.  1870.  London.) 

15.  "  As  theory,  Education  allies  itself  to 
Psychology,  Physiology,  and  Sociology.  The 
materials  of  its  teaching  it  draws  from  these  phi- 
losophies, from  the  practice  of  the  schoolroom, 
and  from  the  rich  domain  of  History.  .  .  . 
I  have  some  sympathy  with  the  cynical  Love 
Peacock,  who,  in  describing  certain  social  bores 
in  the  shape  of  men  of  one  idea  who  hold  forth 
in  season  and  out  of  season,  says  : — i  The  worst 
of  all  bores  was  the  third.  His  subject  had  no 
beginning,  middle,  nor  end.  It  was  Education. 
Never  was  such  a  journey  through  the  desert 
of  mind,  the  great  Sahara  of  intellect.  The 


20  ON  EDUCATION. 

very  recollection  makes  me  thirsty/  Such  men 
are  not  educationists  in  any  sense  in  which  that 
term  is  applicable  within  these  walls.  They  are 
men  of  leisure  who  have  restless  minds,  and  if 
they  have  not  one  fixed  idea  or  crotchet,  will 
find  another.  An  educationist  has  no  crotchets. 
That  man  has  crotchets  who,  having  seized  on 
that  particular  corner  of  a  large  and  many-sided 
subject  which  has  some  secret  affinity  with  his 
own  mind,  or  affords  the  quickest  passage  to  no- 
toriety, pursues  it  to  the  death.  Now,  an  edu- 
cationist is,  by  virtue  of  his  very  name  and  vo- 
cation, inaccessible  to  all  petty  fanaticisms.  He 
has  to  deal  with  a  subject  of  infinite  variety,  and 
so  variously  related  to  life,  that  he  is  more  apt 
to  be  lost  in  hesitations  and  scepticisms  than  to 
be  the  victim  of  a  fixed  idea.  If  you  wish  to 
meet  with  educational  crotchets,  you  must  go  to 
the  specialist  in  this  or  that  department  of 
knowledge,  who  is  unfortunate  enough  to  take 
up  the  question  of  Education,  as  you  see  he 
often  in  moments  of  aberration  takes  up  other 
subjects  which  are  outside  his  own  range  of  in- 
tellectual experience.  It  is  only  in  such  cases 
that  you  will  find  the  confidence  and  self-assur- 
ance which  is  born  of  limited  knowledge,  and 
the  pertinacious  insistence  which  flows  from 
these  habits  of  mind.  To  him  whose  subject  is 
Education  crotchets  are  prohibited,  because  his 
opinions  on  this  or  that  point  are  related  on  the 
one  side  to  rational  and  comprehensive  theory, 
and  on  the  other  to  the  daily  practice  of  the 
schoolroom  and  the  needs  of  life.  .  .  . 


ON   EDUCATION.  21 

The  more  abstract  treatment  of  the  theory  of  Ed- 
ucation is  doubtless,  if  true  in  its  philosophy,  of 
universal  application.  It  sweeps  the  whole  field. 
But  this  will  engage  our  attention  only  within 
carefully  prescribed  limits,  and  when  we  leave 
this  portion  of  our  subject,  we  have  to  restrict 
ourselves  on  all  sides.  The  education  of  every 
human  being  is  determined  by  potent  influences- 
which  do  not  properly  fall  within  the  range  of 
our  consideration  here.  The  breed  of  men  to 
which  the  child  belongs,  the  character  of  his  pa- 
rents, the  human  society  into  which  he  is  born, 
the  physical  circumstances  by  which  he  is  sur- 
rounded, are  silently  but  irresistibly  forming 
him.  The  traditions  of  his  country,  its  popular 
literature,  its  very  idioms  of  speech,  its  laws  and 
customs,  its  religious  life,  its  family  life,  consti- 
tute an  aggregate  of  influence  which  chiefly 
make  him  what  he  is.  ...  By  their  con- 
stant presence  they  mould  the  future  man,  him- 
self unconscious.  They  are  the  atmosphere  of 
the  humanity  of  his  particular  time  and  place, 
and  in  breathing  it  he  is  essentially  a  passive 
agent.  .  .  .  The  passive  activity  of  our  na- 
ture is  not  to  be  ignored  in  our  educational 
methods  ;  it  is  to  be  turned  to  use  as  one  of  our 
most  potent  instruments,  but  it  is  mainly  the 
self-conscious  forces  that  we  have  to  educe  and 
direct.  Even  in  doing  this  we  are  bound  by  ex- 
ternal conditions,  and  must  take  note  not  only  of 
the  almost  irresistible  forces  around  us,  but  of 
minor  conditions  of  time,  place,  and  circum- 
stance. Each  successive  century,  and  the  tra- 


~2  ON   EDUCATION. 

ditions  and  circumstances  of  each  country,  nay, 
the  genius  of  each  people,  present  to  us  the  ed- 
ucational problem  in  ever-changing  aspects. 
Educational  systems  cannot  be  manufactured  in 
the  study.  Our  theory  of  the  end  of  all  educa- 
tion and  the  means  by  which  that  end  has  to  be 
attained  may  be,  or  rather  ought  to  be,  always 
the  same  ;  but  the  application  of  that  theory 
must  vary  with  varying  external  conditions. 
What  present  defects  have  we  here  and  now, 
and  to  what  dangers  are  we  exposed  ?  is  the 
form  which  the  practical  question  must  take  with 
us. ' '  (Laurie,  Inaugural  Address,  Chair  of  Ed- 
ucation, pp.  21-24.  Edinburgh,  1876.) 

16.  "  To  write  upon  education,  means  to 
write  upon  almost  every  thing  at  once  ;  for  it  has 
to  care  for,  and  watch  over,  the  development 
of  an  entire,  though  miniature,  world  in  little, 
— a  microcosm  of  the  microcosm.  All  the  ener- 
gies with  which  nations  have  labored  and  signal- 
ized themselves  once  existed  as  germs  in  the 
hand  of  the  educator.  *If  we  carried  the  sub- 
ject still  further,  every  century,  every  nation, 
and  even  every  boy  and  every  girl,  would  require 
a  distinct  system  of  education,  a  different  primer, 
and  domestic  French  governess,  &c.  .  .  .  But 
although  the  spirit  of  education,  always  watch- 
ing over  the  whole,  is  nothing  more  than  an  en- 
deavor to  liberate,  by  means  of  a  freeman,  the 
ideal  human  being  which  lies  concealed  in  every 
child  ;  and  though,  in  the  application  of  the  di- 
vine to  the  child's  nature,  it  must  scorn  some 
useful  things,  some  seasonable,  individual,  or  im- 


ON  EDUCATION.  23 

mediate  ends  ;  yet  it  must  incorporate  itself  in 
the  most  definite  applications,  in  order  to  be 
clearly  manifested. 

"  But  who  then  educates  in  nations  and 
ages  ? — Both  ! — The  living  time,  which  for 
twenty  or  thirty  years  struggles  unceasingly  with 
men  through  actions  and  opinions,  tossing  them 
to  and  fro  as  with  a  sea  of  waves,  must  soon 
wash  away  or  cover  the  precipitate  of  the  short 
school  years,  in  which  only  one  man,  and  only 
words  taught.  The  century  is  the  spiritual  cli- 
mate of  man,  mere  education  the  hot-house  and 
forcing-pit,  out  of  which  he  is  taken  and  planted 
forever  in  the  other.  By  century  is  here  meant 
the  real  century,  which  may  as  often  truly  con- 
sist of  ten  years,  as  of  ten  thousand,  and  which 
is  dated,  like  religious  eras,  only  from  great  men. 
What  can  insulated  words  do  against  living  pres- 
ent action  ?  The  present  has  for  new  deeds- 
also  new  words  ;  the  teacher  has  only  dead  lan- 
guages for  the,  to  all  appearance,  dead  bodies  of 
his  examples.  The  educator  has  himself  been 
educated,  and  is  already  possessed,  even  without 
his  knowledge,  by  the  spirit  of  the  age,  which  he 
assiduously  labors  to  banish  out  of  the  youth  (as 
a  whole  city  criticises  the  spirit  of  the  whole 
city).  Only,  alas  !  every  one  believes  himself  to 
stand  so  precisely  and  accurately  in  the  zenith  of 
the  universe,  that,  according  to  his  calculation, 
all  suns  and  nations  must  culminate  over  his 
head  ;  and  he  himself,  like  the  countries  at  the 
equator,  cast  no  shadow  save  into  himself 
alone.  .  .  .  The  spirit  of  the  nation  and  of 


24  ON   EDUCATION. 

the  age  decides,  and  is  at  once  the  schoolmaster 
and  the  school  ;  for  it  seizes  on  the  pupil  to 
form  him  with  two  vigorous  hands  and  powers  ; 
with  the  living  lesson  of  action,  and  with  its 
unalterable  unity.  If — to  begin  with  unity — ed- 
ucation must  be,  like  the  Testament,  a  continu- 
ous endeavor  to  withdraw  the  force  of  interrupt- 
ing mixtures,  then  nothing  builds  up  so  strong  as 
the  present,  which  ceases  not  for  a  moment,  and 
eternally  repeats  itself  ;  and  which,  with  joy  and 
sorrow,  with  towns  and  books,  with  friends  and 
enemies,  in  short,  with  thousand-handed  life, 
presses  and  seizes  on  us.  No  teacher  of  the  peo- 
ple continues  so  uniformly  one  with  himself  as 
the  teaching  people.  Minds  molten  into  masses 
lose  something  of  their  free  movements  :  which 
bodies,  for  instance,  that  of  the  world,  perhaps 
that  of  the  universe,  seem  to  gain  by  their  very 
inassiveness,  and,  like  a  heavy  colossus,  to  move 
all  the  more  easily  along  the  old,  iron-covered 
track.  For  however  much  marriages,  old  age, 
deaths  and  enmities,  are  in  the  individual  case 
subject  to  the  law  of  freedom,  yet  in  a  whole  na- 
tion, lists  of  births  and  deaths  can  be  made,  by 
which  it  may  be  shown  that  in  the  canton  of 
Berne  (according  to  Mad.  de  Stael)  the  number 
of  divorces,  as  in  Italy  that  of  murders,  is  the 
same  from  year  to  year.  Must  not,  now,  the 
little  human  being  placed  on  such  an  eternally 
and  ever  similarly  acting  world,  be  borne  as 
upon  a  flying  earth,  where  the  only  directions 
that  a  teacher  can  give  avail  nothing,  because  he 


ON  EDUCATION.  26 

has  first  unconsciously  received  his  line  of  move- 
ment upon  it  ? 

"  Thence,  in  spite  of  all  reformers  and  inform- 
ers, nations,  like  meadows,  reach  ever  a  similar 
verdure  ;  thence,  even  in  capital  cities,  where  all 
school-books  and  schoolmasters,  and  even  par- 
ents of  every  kind,  educate,  the  spirit  main- 
tains itself  unalterably  the  same.  Repetition  is 
the  mother  not  only  of  study,  but  also  of  educa- 
tion. .  .  .  Certainly  one  might  say  that  also 
in  families  there  educates,  besides  the  popular 
masses,  a  pedagogic  crowd  of  people  ;  at  least, 
for  instance,  aunt,  grandfathers,  grandmothers, 
father,  mother,  god-parents,  friends  of  the  fam- 
ily, the  yearly  domestics,  and  at  the  end  of  all 
the  instructor  beckons  with  his  forefinger,  so  that 
— could  this  force  continue  as  long  as  it  would 
gladly  be  maintained — a  child,  under  these  many 
masters,  would  resemble,  much  more  than  one 
thinks,  an  Indian  slave,  who  wanders  about  with 
the  inburnt  stamps  of  his  various  masters.  But 
how  does  the  multitude  disappear  compared 
with  the  higher  one,  by  which  it  was  colored  ; 
just  as  all  the  burnt  marks  of  the  slave  yet  can- 
not overcome  the  hot  black  coloring  of  the  sun, 
but  receive  it  as  a  coat  of  arms  in  a  sable  field  ? 
.  .  .  The  end  desired  must  be  known  before 
the  way.  All  means  or  arts  of  education  will 
be,  in  the  first  instance,  determined  by  the  ideal 
or  archetype  we  entertain  of  it.  But  there  floats 
before  common  parents,  instead  of  one  arche- 
type, a  whole  picture  cabinet  of  ideals,  which 
they  impart  bit  by  bit,  and  tattoo  into  their 


26  OK   EDUCATION. 

children.  If  the  secret  variances  of  a  large  class 
of  ordinary  fathers  were  brought  to  light,  and 
laid  down  as  a  plan  of  studies,  and  reading  cata- 
logue for  a  moral  education,  they  would  run 
somewhat  after  this  fashion  : — In  the  first  hour 
pure  morality  must  be  read  to  the  child,  either 
by  myself,  or  the  tutor  ;  in  the  second,  mixed 
morality,  or  that  which  may  be  applied  to  one's 
own  advantage  ;  in  the  third,  *  Do  you  not  see 
that  your  father  does  so  and  so  ? '  in  the  fourth, 
'  You  are  little,  and  this  is  only  fit  for  grown- 
up people  ;'  in  the  fifth,  i  The  chief  matter  is 
that  you  should  succeed  in  the  world,  and  be- 
come something  in  the  state  ;'  in  the  sixth, 
*  Not  the  temporary,  but  the  eternal,  determines 
the  worth  of  a  man  ;'  in  the  seventh,  i  Therefore 
rather  suffer  injustice,  and  be  kind  ;'  in  the 
eighth,  '  but  defend  yourself  bravely  if  any  one 
attack  you  ;'  in  the  ninth,  i  Do  not  make  such  a 
noise,  dear  child  ;'  in  the  tenth,  l  A  boy  must 
not  sit  so  quiet  ;7  in  the  eleventh,  '  You  must 
obey  your  parents  better  ;'  in  the  twelfth,  '  and 
educate  yourself.1  So  by  the  hourly  change  of 
his  principles  the  father  conceals  their  untena- 
bleness  and  one-sidedness.  As  for  his  wife,  she 
is  neither  like  him,  nor  yet  like  that  harlequin 
who  came  on  to  the  stage  with  a  bundle  of  pa- 
pers under  each  arm,  and  answered  to  the  in- 
quiry what  he  had  under  his  right  arm,  '  orders, ' 
and  to  what  he  had  under  his  left,  '  counter- 
orders  ;'  but  the  mother  might  be  much  better 
compared  to  a  giant  Briareus,  who  had  a  hun- 
dred arms,  and  a  bundle  of  papers  under  each. 


ON   EDUCATION.  27 

The  majority  of  educated  men  are, 
therefore,  at  present  an  illumination  which  burns 
off  by  fits  and  starts  in  the  rain,  shining  with  in- 
terrupted forms,  and  depicting  broken  charac- 
ters. But  the  bad  and  impure  spirits  of  educa- 
tional systems  are  yet  to  be  reduced  into  other 
divisions.  Many  parents  educate  their  children 
only  for  themselves, — that  is,  to  be  pretty 
blocks,  or  soul-alarums,  which  are  not  set  to 
move  or  sound  when  stillness  is  required.  The 
child  has  merely  to  be  that  on  which  the  teacher 
can  sleep  most  softly  or  drum  most  loudly  ;  who, 
having  something  else  to  do  and  to  enjoy,  wishes 
to  be  spared  the  trouble  of  education,  duly  but 
most  unreasonably  expecting  its  fruits. 
Related  to  those  teachers  who  wished  to  be  ma- 
chine-makers are  the  educators  for  appearances 
and  political  usefulness.  Their  maxims,  thor- 
oughly carried  out,  would  only  produce  pupils, 
or  rather  sucklings,  passively  obedient,  boneless, 
well -trained,  patient  of  all  things, — the  thick, 
hard,  human  kernel  would  give  place  to  the 
soft,  sweet  fruit-pulp, — and  the  child's  clod  of 
earth,  into  which  growing  life  should  breathe  a 
divine  spirit,  would  be  kept  down  and  manured 
as  though  it  were  but  a  corn-field, — the  edifice 
of  the  state  would  be  inhabited  by  mere  spin- 
ning-machines, calculating-machines,  printing 
and  pumping  apparatus,  oil-mills,  and  models, 
for  mills,  pumps,  and  spinning-machines,  &c. 
Education  can  neither  entirely  consist 
of  mere  unfolding  in  general,  or,  as  it  is  now 
better  called,  excitement, — for  every  continued 


28  ON   EDUCATION. 

existence  unfolds,  and  every  bad  education  ex- 
cites, just  as  oxygen  positively  irritates, — nor  in 
the  unfolding  of  all  the  powers,  because  we  can 
never  act  upon  the  whole  amount  of  them  at 
once  ;  as  little  as  in  the  body  susceptibility  and 
spontaneity,  or  the  muscular  and  nervous  system, 
can  be  strengthened  at  the  same  time."  (Rich- 
ter,  Levana,  Preface,  ix,  and  pp.  7-33.  Boston. 
1863.) 

17.  "  A  treatise  on  education  does  not  in- 
clude the  theory  of  instruction,  whose  wide  realm 
embraces  the  mistakes  of  all  sciences  and  arts  ; 
nor  the  theory  of  remedies,  which  would  require 
libraries  instead  of  volumes  for  the  complication 
of  mistakes,  years,  positions,  and  relations.     At 
the  same  time  no  science  is  entirely  disconnected 
from  the  rest  ;  the  feet  cannot  move  without  the 
hands."      (Ibid.,  p.  390.) 

18.  The  education  that  any  one  receives  de- 
pends upon  the  ethical  relations  by  which  he  is 
surrounded.     But    education    must    regard   the 
nature  and  powers  of  the  mind  of  him  who  is  to 
be  educated.     Hence  education,  as  a  product,  is 
founded   upon   ethical   relations   upon   the    one 
hand,  and  the  nature  of  mind,  or  Psychology, 
upon  the  other.     Education,  in  part,  is  depend- 
ent upon  teaching  or  instruction  as  a  means  for 
securing    its    ends.     Teaching,     then,     directly 
busies  itself  with  the  subject-matter  that  is  to  be 
learned,  and  with  the  mind  which  is  to  learn  it. 

19.  "  The  educator  of  youth  does  not  merely 
communicate  so  much  instruction  from  year  to 
year  ;  he  develops  the  receptive  and  acquisitive 


ON   EDUCATION. 


29 


tendencies  of  mind,  which  are  afterwards  to 
play  their  part  in  the  intellectual  activity  of  the 
nation.  He  trains  the  intelligence  of  those  who 
are  afterwards  to  be  the  teachers  of  others,  as 
well  as  of  those  who  are  only  to  be  interested  in- 
quirers after  truth.  "  (Calderwood,  On  Teach- 
ing,  p.  49,  ed.  1875,  New  York.) 


in. 

ON  TEACHING. 

20.  Having  briefly  considered  the  notion  of 
the  terms  Pedagogics  and  Education,  the  reader 
is  directed  to  the  conception  of  the  term  Teach- 
ing. 

Thought  is  the  modification  of  the  activity 
called  Intelligence,  and  Language  is  its  Form. 
Language  is  the  mirror  which  reflects  the  ideas 
that  are  in  the  mind  of  him  who  utters  it.  Lan- 
guage is  a  record  of  thought.  Language,  in  its 
widest  signification,  is  the  instrument  for  per- 
petuating the  life  of  a  nation,  or  rather  it  is  the 
life  of  a  people  perpetuated.  Language  is  the 
form  of  the  matter  which  once  existed  in  the 
consciousness  of  the  person  who  uttered  it  ;  it  is 
a  product  of  thought  ;  perhaps  more  exactly  it 
is  thought  itself.  "It  is  only  as  there  is  a 
XoyoS  in  the  outer  world,  answering  to  the 
XoyoS  or  internal  reason  of  the  parties,  that  men 
can  come  into  a  mutual  understanding  in  regard 
to  any  thought-state  whatever."  (Grindon, 
Life,  p.  349.) 

"  By  Language  we  do  not  mean  the  mere  art 
of  speaking  and  writing  according  to  some 
specific,  arbitrary  mode,  which  though  intelli- 


ON  TEACHING.  31 

gible  in  one  country,  is  unintelligible  in  another. 
We  mean  that  beautiful  and  inevitable  flowering 
forth  in  speech  of  the  inner,  living  intellect  of 
man,  which,  older  and  more  excellent  than  all 
prosody  and  spelling,  is  an  integral  work  of  na- 
ture ;  and  which,  wen.,  ^  possible  for  the  acci- 
dental forms  which  it  may  hold  at  any  given 
epoch,  as  English  and  French,  Latin  and  Greek, 
to  be  suddenly  and  totally  abolished,  would  in 
itself  be  unaffected,  and  speedily  incarnate 
afresh,  unchanged  save  in  the  extrinsic  circum- 
stances of  costume."  (Ibid,  pp.  153,  154,  third 
ed.,  London.)  Nations  differ  in  their  language 
— these  differences  measure  those  differences 
that  exist  among  the  ideas  or  notions  which  are 
substantially  common  to  many  peoples.  The 
content  and  extent  of  words  having  the  same 
general  meaning,  when  expressed  in  different 
languages,  are  hardly  equivalent  nor  precisely 
identical.  No  two  nations  live  and  act  exactly 
alike,  and  as  language  follows  life,  it  is  but  in 
the  harmony  of  things  that  this  should  occasion 
different  notions  of  life  and  -actions  in  the  minds 
of  the  various  peoples,  and  hence  in  language. 
Two  or  three  examples  will  illustrate  the  case  : 

21.  To  indicate  a  certain  notion,  the  Greeks 
used  deiknumi,  the  English  equivalents  of  which 
are  :  "  To  bring  to  light,  to  display,  to  portray, 
to  represent  to  the  life  as  in  statuary,  to  shew, 
to  point  out,  to  make  known  by  words,  to  tell, 
to  explain,  to  teach,  to  prove,  to  offer,  to  prof- 
fer." Buttmann  traces  the  prefix  deik  to  a  root 
dek,  which  contains  the  common  notion  of 


32  ON   TEACHING. 

stretching  out  the  right  hand  either  to  point, 
or  to  welcome,  (Liddell  and  Scott,  Greek- 
English  Lexicon ,  Oxford,  1871.)  The  essential 
idea  seems  to  rest  upon  the  action  of  pointing 
to,  or  towards,  a  thing.  The  Greeks  cultivated 
the  graces  of  action  as  well  as  the  harmony  of 
sounds,  and  it  is  not  difficult  to  conceive  the 
elders  among  the  people  pointing  out,  showing, 
portraying  as  artists,  the  things  before  them  to 
the  youth,  much  as  a  traveller  would  do  at  the 
present  time  to  a  youthful  companion.  The  fact 
that  Socrates  was  at  so  great  pains  to  develop  in 
his  pupils  the  power  to  reason  would  argue  that, 
in  his  opinion,  before  his  time  the  powers  of  per- 
ception and  memory  of  the  youth  had  been  rec- 
ognized as  of  greater  value  in  acquiring  an  edu- 
cation than  the  reflective  powers.  The  word 
teaching  also  appears  to  exhibit  some  one  as  in 
the  action  of  directing  the  attention  of  another 
to  something  through,  or  by  means  of,  the  ges- 
tures of  his  right  hand — it  does  not  so  much 
seem  to  exhibit  one  as  showing  a  thing,  object, 
immediately  and  directly,  as  it  shows  indirectly 
through  words  and  general  gestures,  and  by  illus- 
trative sketches — it  implies  an  exhortation  to  at- 
tend to  this  thing  which  is  in  mind  as  a  philo- 
sophical truth.  It  would  seem  to  indicate  an  ex- 
planation of  memorized  words.  "  When  the 
children  could  read,  and  understand  what  they 
read,  the  works  of  the  poets  were  put  in  requi- 
sition, to  exercise  their  minds,  and  awaken  their 
hearts  to  great  and  noble  deeds.  Plato,  Leg. 
vii.  p.  810,  approves  of  this,  and  also  recom- 


OK  TEACHING.  33 

mends  committing  whole  poems,  or  select  pas- 
sages, to  memory  ;  and  this  method  of  instruc- 
tion appears  to  have  been  universal.  Above  all, 
the  poems  of  Homer  were  thought  to  contain, 
by  precept  and  example,  every  thing  calculated 
to  awaken  national  spirit,  and  to  instruct  a  man 
how  to  be  beautiful  and  good."  (Becker, 
Charicles,  trans,  by  Frederick  Metcalfe,  ed. 
1866,  p.  233.) 

22.  The  Latins  conveyed  a  certain  notion  by 
doceo,  which  is  rendered  in  English  by  :  "  To 
teach,  to  inform,  to  instruct,  to  show,  to  point 
out,  to  represent,  to  exhibit. "  It  is  compared 
with  edocere,  which  means  "  to  make  one  learn, 
to  make  acquainted  with,  more  energetic  than 
docere."  Perdocere  means  "  to  teach  per- 
fectly, to  instruct  thoroughly."  Erudire  im- 
plies * '  to  initiate  in  learning. ' '  Instruct,  in  and 
struo,  means  :  To  join  together,  to  pile  tip, 
heap  up,  to  erect,  to  build,  to  set  in  array,  to 
join  together,  to  construct.  (Bullion,  Lat.-Eng. 
Diet.,  ed.  1869.)  The  essential  .idea  with  the 
Latins  seems  to  be  that  of  laying  before  one 
some  matters  as  objects  to  be  seen,  handled, 
piled  up  in  layers  one  upon  another  (instruct), 
to  show  as  in  an  exhibition.  The  word  pictures 
one  as  standing  at  work  upon  some  visible  ob- 
jects, and  calling  the  attention  of  another  to  these 
objects  as  he  piles  them  up,  one1  upon  another. 
This  sense  is  virtually  different  from  the  thought 
with  the  Greeks,  who  rather  withdrew  them- 
selves from  the  presence  of  the  things  about 
which  they  discoursed,  and  crowded  the  thought 


34  OK   TEACHING. 

home  to  the  conviction  of  the  hearer  by  words 
and  exhortatory  gestures  of  the  right  hand. 
This  notion  of  doceo  corresponds  with  the  gene- 
ral characteristics  of  the  Latins,  who  were  a  peo- 
ple pre-eminently  skilful  in  the  affairs  of  practi- 
cal business.  They  regarded  the  objects  of  bus- 
iness directly,  rather  than  through  philosophy. 
Hence,  the  one  would  instruct  a  youth  in  law  by 
exhibiting  to  him  law  practice  in  the  courts, 
while  the  other  would  lecture  the  youth  about 
the  principles  of  law  in  the  abstract,  while  seated 
in  his  stone  chair,  or  while  walking  about  the 
groves. 

23.  The  Anglo-Saxons  expressed  a  certain 
notion  by  the  word  t&can,  which  is  rendered  in 
English  :  "  To  teach,  to  instruct,  to  show,  to  di- 
rect, to  command,  to  see  to,  to  provide,  to  or- 
der, to  convince,  to  prove."  (Bosworth,  An- 
glo-Saxon and  Eng.  Diet.,  London,  1860.)  In 
this  case  the  notion  has  an  element  of  poiver  and 
authority  in  it  ;  it  shows,  with  power  to  com- 
mand attention  ;  it  directs,  but  it  is  imperative 
about  something  towards  somebody  ;  it  does  not 
simply  exhort  the  attention  of  somebody  towards 
an  idea  by  the  right  hand  in  persuasion  or  wel- 
come, as  does  the  Greek  deiknumi — nor  does 
it  call  the  attention  of  somebody  to  what  the  ex- 
hibitor has  before  him,  piling  it  up  in  order,  as 
do  the  Latin  doceo  and  instruo ;  but  it  shows 
something  to  somebody,  meaning  that  this  some- 
body shall  attend  to  this  something.  This  word 
tgecan  discloses  the  characteristic  trait  of  the 
Anglo-Saxon  life,  the  disposition  to  do  something 


ON  TEACHING.  35 

for  another,  and  then  to  command  him  to  respect 
what  has  been  placed  before  him.  The  word  re- 
gards with  emphasis  both  what  is  provided,  and 
him  for  whom  it  is  provided. 

24.  These  three  instances  illustrate  the  differ- . 
ences  which  exist  among  peoples  when  they  ex- 
press a  notion  that  is  ordinarily  regarded  as  the 
same  by  them  all.  Each  people  has  its  own  set- 
ting of  thoughts  which  control  the  form,  and  as- 
sist in  conserving  the  meaning  of  subsequent  no- 
tions. These  thoughts,  notions,  conserved  in 
form,  are  language.  The  words  "  instruct  "  and 
"  teach'7  are  both  in  common  use  at  this  time, 
practically  as  synonyms7.  Following  the  lines  of 
their  ancestry,  and  considering  the  tendency  of 
the  present  age,  it  is  determined  to  use  the  word 
teaching  rather  than  instruction  in  the  expres- 
sion Methods  of  Teaching.  As  illustrating  the 
deep-seated  element  of  authority  which  exists  in 
the  Anglo-Saxon  notion  of  teaching,  the  follow- 
ing quotations  are  subjoined  : 

26.  "I  hope  I  may  be  excused  for  one  re- 
mark on  a  tendency  in  education  at  present, 
more  especially  with  regard  to  the  modern  sub- 
jects, to  render  the  process  interesting,  as  it  is 
usually  called,  but  amusing  would  probably  be 
the  more  correct  word.  It  would  be  absurd  to 
recommend  that  any  subject  should  be  proposed 
in  a  purposely  repulsive  form  to  students,  espec- 
ially to  youth  ;  but,  on  the  other  hand,  it  seems 
to  me  a  most  enervating  practice  to  shrink  from 
demanding  even  irksome  attention  whenever  it  is 
necessary.  The  lesson  that  success  in  any  pur- 


36  ON   TEACHING. 

suit  demands  serious  toil  must  be  learned  eventu- 
ally, and  like  most  lessons  is  learned  with  least 
pain  in  early  years. "  (Todhunter,  Conflict  of 
Studies  and  other  Essays,  p7  21.  London, 
1873.) 

26.  "  Parents  and  the  public  have  little  idea 
how  close  a  resemblance  there  is  between  teach- 
ing and  writing  on  the  sands  of  the  sea,  unless 
either  there  is  a  distinct  capacity  for  learning  on 
the  part  of  the  pupil,   or  some  system  of  ex- 
amination and  reward  to  force  the  pupil  to  ap- 
ply. "     (Jevons,  paper  in  Mind,  p.  195,  No.  VI., 
April,  1877.)     (Reinserted   under  Memory  and 
"Cram,"  §  172.) 

27.  u  Whatever  the  age  and  attainment  of 
the  pupils  under  charge,  the  first  requisite  for 
communicating  instruction  is  to  gain  and  keep 
their    attention.     Teaching,   to    be    successful, 
must  therefore  be  adapted  to  win  attention.     At 
the  earlier  stages  of  school  life  this  is  the  one 
pressing  require-ment.     Somehow,  attention  must 
be  made  possible  even  to  the  most  restless  little 
ones,  to  whom  the  first  restraints  of  school  life 
are  irksome.     Accustomed   to  have  every  new 
object  attract  their  interest  just  as  long  as  they 
recognized  any  thing  attractive  in  it — permitted 
to  change  from  one  engagement  to  another  as 
caprice  dictated — they  must  be   made   familiar 
with  restriction.     They  must  begin  to  be  regu- 
lated by  the  will  of  another.     Taking  this  as 
self-evident,  we  are  prone  to  say  that  they  must 
do  so,  whether  they  will  or  not.     This  is  one  of 
our  superficial  current  phrases  which  cover  over 


ON  TEACHING.  37 

many  points  needing  careful  consideration.  At- 
tention is  not  to  be  secured  by  mere  exercise  of 
authority.  Authority  has  a  great  deal  to  do 
through  the  whole  course  of  school  life,  but  we 
cannot  '  command '  attention,  as  we  say,  by 
merely  demanding  that  it  be  given.  A  radical 
mistake  is  made  if  a  teacher  lean  on  his  authority 
in  the  school  as  the  guarantee  for  attention  by  the 
scholars.  He  must  consider  the  requirements 
of  the  undisciplined  mind,  and  adapt  himself  to 
them.  Children  attend  to  what  interests  them. 
This  must  determine  the  kind  of  assistance  to- 
be  given  them  in  acquiring  habits  of  attention. 
To  help  them  in  this  is  an  obvious  part  of  a 
teacher's  work.  .  .  .  The  master  of  a  school 
in  this  respect  shares  a  task  which  is  common  to 
all  who  essay  to  teach  others.  In  this  appears 
the  true  place  and  power  of  the  profession.'* 
(Calderwood,  On  Teaching,  pp.  47-49,  ed.  1875.) 
28.  The  conception  of  Teaching  which  pre- 
vails in  these  inquiries  is  limited  to  that  assistance 
which  one  person  (teacher)  consciously  gives  to 
another  person  or  thing  (learner),  when  this  lat- 
ter is  learning  something.  Teachers  are  not 
necessarily  educators.  Any  thing  educates  the 
child  that  helps  to  mould  its  character,  or  that 
stimulates  its  self-control.  Fire  educates  in  an 
imperative  manner,  but  it  does  not  teach.  The 
authority  of  the  parent  educates  his  child,  while 
the  child  may  be  taught  nothing  in  regard  to  the 
nature  or  source  of  authority.  A  teacher's  per- 
sonal influence  may  educate  a  school  in  ways  of 
virtue,  while  he  has  taught  them  nothing  about  the 


38  OK  TEACHING. 

nature  of  virtue.  Teaching  regards  the  purely 
intellectual  capacities  of  Man.  Education  refers 
to  all  the  capabilities  of  Mind.  The  intellect  is 
taught  by  a  person,  and  educated  by  persons  and 
things.  The  will  is  educated  by  any  power. 
Teaching  sets  the  subject-matter,  trusting  the 
mind  to  accept  the  truth  ;  educating  may  exert 
a  power  without  giving  any  reason  or  instruc- 
tion. Teachers  should  be  educators.  Parents 
are  educators — they  may  also  be  teachers.  Good 
teaching  and  good  educating  put  the  mind  of 
him  who  is  taught  or  educated,  into  a  frame 
which  acknowledges  and  accepts  testimony  and 
authority  from  whatever  source  they  spring. 
That  teaching  or  educating  is  pernicious  which 
leaves  the  mind  of  the  learner  in  a  state  of  un- 
due skepticism  towards  testimony  and  authority. 
(See  §§  31-34.) 

29.  "  The  communication  of  knowledge  in 
general  is  the  common  idea  by  which  these 
words — inform^  instruct,  teach— &IQ  connect- 
ed with  each  other.  Inform  is  the  general  term  ; 
the  other  two  are  specifick.  To  inform  is  the 
act  of  persons  in  all  conditions  ;  to  instruct  and 
teach  are  the  acts  of  superiours,  either  on  one 
ground  or  another  :  one  informs  by  virtue  of  an 
accidental  superiority  or  priority  of  knowledge  ; 
one  instructs  by  virtue  of  superior  knowledge, 
or  superior  station  :  one  teaches  by  virtue  of 
superiour  knowledge,  rather  than  station  :  diplo- 
matick  ao-ents  inform  their  governments  of  the  po- 
litical transactions  in  which  they  are  concerned  ; 
government  instructs  its  different  functionaries 


ON  TEACHING.  39 

and  officers  in  regard  to  their  mode  of  proceed- 
ing  ;  professors  and  preceptors  teach  those  who 
attend  a  publick  school  to  learn. 

'  i  To  inform  is  applicable  to  matters  of  general 
interest ;  we  may  inform  ourselves  or  others  on 
every  thing  which  is  a  subject  of  inquiry  or  curios- 
ity ;  and  the  information  serves  either  to  amuse 
or  to  improve  the  mind  ;  to  instruct  is  applica- 
ble to  matters  of  serious  concern,  or  that  which 
is  practically  useful  ;  it  serves  to  set  us  right  in 
the  path  of  life.  A  parent  instructs  his  child  in 
the  course  of  conduct  he  should  pursue  ;  a  good 
child  profits  by  the  instruction  of  a  good  parent 
to  make  him  wiser  and  better  for  the  time  to 
come  ;  to  teach  respects  matters  of  art  and 
science  ;  the  learner  depends  upon  the  teacher 
for  the  formation  of  his  mind,  and  the  establish- 
ment of  his  principles.  Every  one  ought  to  be 
properly  informed  before  he  pretends  to  give  an 
opinion  ;  the  young  and  inexperienced  must  be 
instructed  before  they  can  act ;  the  ignorant 
must  be  taught,  in  order  to  guard  them  against 
errour.  Truth  and  sincerity  are  all  that  is  neces- 
sary for  an  informant ;  general  experience  and 
a  perfect  knowledge  of  the  subject  in  question 
are  requisite  for  the  instructor;  fundamental 
knowledge  is  requisite  for  the  teacher.  Those 
who  give  information  upon  the  authority  of 
others  are  liable  to  mislead  ;  those  who  instruct 
others  in  doing  that  which  is  bad,  scandalously 
abuse  the  authority  that  is  reposed  in  them  ; 
those  who  pretend  to  teach  what  they  themselves 


40  ON  TEACHING. 

do  not  understand,  mostly  betray  their  ignorance 
sooner  or  later. 

"  To  inform  and  to  teach  are  employed  for 
things  as  well  as  persons  ;  to  instruct  only  for 
persons  :  books  and  reading  inform  the  mind  ; 
history  or  experience  teaches  mankind. ' '  (Crabb, 
Synonyms,  ed.  1859.) 

30.  "Inform  (Lat.  in  and  forma,  shape  or 
form)  relates  only  to  matters  of  fact  made  known 
to  one  who  could  not  have  known  them  before. 
Instruction  (Lat.  instruere,  instructus)  relates 
to  principles  drawn  from  known  facts.  Teach- 
ing (A.  S.  t#can,  to  teach),  as  distinct  from 
instruction,  is  applied  to  practice  (it  may  be  the 
practice  of  an  art  or  branch  of  knowledge).  A 
child  is  instructed  in  grammar,  and  taught  to 
speak  a  language.  Teach  has  a  purely  mechani- 
cal application,  which  does  not  belong  to  instruct. 
A  dog  may  be  taught  a  trick  ;  but  he  could  not 
be  instructed  in  any  thing.  The  two  processes 
of  teaching  and  instruction  may  thus  go  on 
simultaneously.  In  mathematics  there  is  no  in- 
formation, because  the  propositions  are  not  state- 
ments of  fact,  but  are  based  upon  principles 
assumed.  .  Information  is  of  new  facts  ;  instruc- 
tion is  of  undeveloped  truths.  Information 
extends  knowledge  ;  instruction  gives  additional 
understanding ;  teaching,  additional  power  of 
doing.  Acquaint  (Fr.  accointer,  Lat.  accognit- 
are,  from  cognosce,  cognitus,  to  know),  Apprise 
(Fr.  appris,  from  apprendre,  the  Lat.  appre- 
hendere ),  and  Advise  ( Fr.  aviser,  Lat.  ad  and 
videre,  visus,  to  see)  closely  resemble  inform, 


ON  TEACHING.  41 

inasmuch  as  they  relate  to  the  communication  of 
matters  of  fact.  I  inform  a  man  when  I  simply 
tell  him  a  fact  which  he  did  not  know  before. 
I  acquaint  him  with  that  of  which  I  furnish 
him  with  all  the  details.  So  I  inform  him  of  the 
fact,  and  acquaint  him  with  the  particulars  of  it. 
I  apprise  him  of  what  particularly  concerns  him 
to  know,  whether  it  be  a  good  or  an  evil,  or  a 
danger,  or  a  probability  of  any  sort.  I  advise 
him  of  that  which  I  impart  to  him  formally, 
officially,  or  as  in  duty  bound,  of  what  occurs  in 
due  course. "  (Smith,  Syn.  Discr.) 


IV. 

ON   AUTHORITIES. 

31.  il  So  in  literature,  men  of  established  re- 
putation, of  classical  merit,  and  known  veracity, 
are    quoted  as  authorities  in   support  of   any 
position/7     (Crabb,  Synonyms.} 

32.  "  Authority    may    come    from    superior 
knowledge  or  information,   or  from   natural  as 
well    as    social     or    professional    relationship/* 
(Smith,  Synonyms  Discriminated.) 

33.  "  The  Principle  of  Authority.—4  The 
principle  of  adopting  the  belief  of  others,  on  a 
matter  of  opinion,  without  reference  to  the  par- 
ticular grounds  on  which  the  belief  may  rest/ 

"  The  Argument  from  Authority. — It  is  an 
argument  for  the  truth  of  an  opinion  that  it  has 
been  embraced  by  all  men,  In  all  ages,  and  in  all 
nations.  Quod  semper,  ubique,  et  ab  omni- 
bus, are  the  morks  of  universality,  according  to 
Vincentius  Lirinensis.  l  This  word  is  sometimes 
employed  in  its  primary  sense,  when  we  refer  to 
any  one's  example,  testimony,  or  judgment  ;  as 
when,  e.g.,  we  speak  of  correcting  a  reading  in 
some  book  on  the  authority  of  an  ancient  MS., 
or  giving  a  statement  of  some  fact  on  the  author- 
ity of  such  and  such  historians,  etc.  In  this 


ON   AUTHORITIES.  43 

sense  the  word  answers  pretty  nearly  to  the  Lat- 
in auetoritas.  It  is  a  claim  to  deference.  Some- 
times, again,  it  is  employed  as  equivalent  to 
potestas,  power,  as  when  we  speak  of  the 
authority  of  a  magistrate.  This  is  a  claim  to 
obedience. ' 

"  Consent. — '  Believing  in  the  prophets  and 
evangelists  with  a  calm  and  settled  faith,  with 
that  consent  of  the  will,  and  heart,  and  under- 
standing, which  constitutes  religious  belief,  I 
find  in  them  the  clear  annunciation  of  the  king- 
dom of  God  upon  earth. ' 

"  Assent  is  the  consequence  of  a  conviction 
of  the  understanding.  Consent  arises  from  the 
state  of  the  disposition  and  the  will.  The  one 
accepts  what  is  true;  the  other  embraces  it  as 
true  and  good  and  worthy  of  all  acceptation.  ... 

i  i  i  These  things  are  to  be  regarded  as  first 
truths,  the  credit  of  which  is  not  derived  from 
other  truths,  but  is  inherent  in  themselves.  As 
for  probable  truths,  they  are  such  as  are  admitted 
by  all  men,  or  by  the  generality  of  men,  or  by 
wise  men  ;  and  among  these  last,  either  by  all 
the  wise,  or  by  the  generality  of  the  wise,  or  by 
such  of  the  wise  as  are  of  the  highest  authority.' 

"  Assent  is  that  act  of  the  mind  by  which  we 
accept  as  true  a  proposition,  a  perception,  or  an 
idea.  It  is  a  necessary  part  of  judgment  ;  for  if 
you  take  away  from  judgment  affirmation  or  de- 
nial, nothing  remains  but  a  simple  conception 
without  logical  value,  or  a  proposition  which 
must  be  examined  before  it  can  be  admitted.  It 
is  also  implied  in  perception,  which  would 


44  ON   AUTHORITIES. 

otherwise  be  a  mere  phenomenon  which  the  mind 
had  not  accepted  as  true. 

* l  Assent  is  free  when  it  is  not  the  unavoidable 
result  of  evidence,  necessary  when  I  cannot 
withhold  it  without  contradicting  myself.  The 
Stoics,  while  they  admitted  that  most  of  our 
ideas  came  from  without,  thought  that  images 
purely  sensible  could  not^be  converted  into  real 
cognitions  without  a  spontaneous  act  of  the 
mind,  which  is  just  assent  or  belief. 
'  Assent  of  the  mind  to  truth  is,  in  all  cases,  the 
work  not  of  the  understanding ,  but  of  the 
reason.  Men  are  not  convinced  by  syllogisms  ; 
but  when  they  believe  a  principle,  or  wish  to  be- 
lieve, then  syllogisms  are  brought  in  to  prove  it.' 

"  Belief. — '  Belief ,  assent,  conviction,  are 
words  which  I  do  not  think  admit  of  logical  defi- 
nition, because  the  operation  of  mind  signified  by 
them  is  perfectly  simple,  and  of  its  own  kind. 
Belief  must  have  an  object.  For  he  who  believes 
must  believe  something,  and  that  which  he  be- 
lieves is  the  object  of  his  belief.  Belief  is  always 
expressed  in  language  by  a  proposition  wherein 
something  is  affirmed  or  denied.  Belief  admits 
of  all  degrees,  from  the  slightest  suspicion  to  the 
fullest  assurance.  There  are  many  operations  of 
mind  of  which  it  is  an  essential  ingredient,  as 
consciousness,  perception,  remembrance.  We 
give  the  name  of  evidence  to  whatever  is  a 
ground  of  belief.  What  this  evidence  is,  is  more 
easily  felt  than  described.  The  common  occa- 
sions of  life  lead  us  to  distinguish  evidence  into 
different  kinds  ;  such  as  the  evidence  of  sense, 


0]$"   AUTHORITIES.  45 

of  memory,  of  consciousness,  of  testimony,  of 
axioms,  and  of  reasoning.  I  am  not  able  to  find 
any  common  nature  to  which  they  may  all  be 
reduced.  They  seem  to  me  to  agree  only  in  this, 
that  they  are  all  fitted  by  nature  to  produce 
belief  in  the  human  mind,  some  of  them  in  the 
highest  degree,  which  we  call  certainty,  others  in 
various  degrees  according  to  circumstances. ' 

' '  St.  Austin  accurately  says,  *  We  know  what 
rests  upon  reason ;  we  believe  what  rests  upon 
authority. '  The  original  data  of  reason  do  not 
rest  upon  reason,  but  are  necessarily  accepted 
by  reason  on  the  authority  of  what  is  beyond 
itself.  These  data  are,  therefore,  in  rigid  pro- 
priety, beliefs  or  trusts.  Thus  it  is,  that  in  the 
last  resort,  we  must,  perforce,  philosophically 
admit,  that  belief  is  the  primary  condition  of  rea- 
son, and  not  reason  the  ultimate  ground  of  belief. 
We  are  compelled  to  surrender  the  proud  Intel- 
lige  ut  credas  of  Abelard,  to  content  ourselves 
with  the  humble  Crede  ut  intelligas  of  Anselm. 

"  To  believe  is  to  admit  a  thing  as  true,  on 
grounds  sufficient,  subjectively;  insufficient, 
objectively.  The  word  believing  has  been 
variously  and  loosely  employed.  It  is  frequently 
used  to  denote  states  of  consciousness  which 
have  already  their  separate  and  appropriate  ap- 
pellations. Thus  it  is  sometimes  said,  I  believe 
in  my  own  existence  and  the  existence  of  an  ex- 
ternal world,  I  believe  in  the  facts  of  nature, 
the  axioms  of  geometry,  the  affections  of  my 
own  mind,  as  well  as,  I  believe  in  the  testimony 


46  ON   AUTHOKITIES. 

of  witnesses,  or  in  the  evidence  of  historical 
documents. 

"  Setting  aside  this  loose  application  of  the 
term,  I  propose  to  confine  it,  first,  to  the  effect 
on  the  mind  of  the  premises  in  what  is  termed 
probable  reasoning,  or  what  I  have  named  con- 
tingent reasoning — in  a  word,  the  premises  of  all 
reasoning,  but  that  which  is  demonstrative  ;  and, 
secondly,  to  the  state  of  holding  true  when  that 
state,  far  from  being  the  effect  of  any  premises 
discerned  by  the  mind,  is  dissociated  from  all 
evidence.  I  propose  to  restrict  the  term  belief 
to  the  assent  to  propositions,  and  demarcate  it 
from  those  inferences  which  are  made  in  the 
presence  of  objects  and  have  reference  to  them. 
I  would  say,  we  believe  in  the  proposition  '  Fire 
burns, '  but  know  the  fact  that  the  paper  about 
to  be  thrust  into  the  flame  will  ignite."  (Flem- 
ing, Vocab.  of  Phil.) 

34.  "  Another  error  is  a  conceit  that  of  for- 
mer opinions  or  sects  after  variety  and  examina- 
tion the  best  hath  still  prevailed  and  suppressed 
the  rest  ;  so  as  if  a  man  should  begin  the  labour 
of  a  new  search,  he  were  but  like  to  light  upon 
somewhat  formerly  rejected,  and  by  rejection 
brought  into  oblivion  :  as  if  the  multitude,  or 
the  wisest  for  the  multitude's  sake,  were  not 
ready  to  give  passage  rather  to  that  which  is 
popular  and  superficial,  than  to  that  which  is 
substantial  and  profound  ;  for  the  truth  is,  that 
time  seemeth  to  be  of  the  nature  of  a  river  or 
stream,  which  carrieth  down  to  us  that  which  is 


ON   AUTHOKITIES.  47 

light  and  blown  up,  and  sinketh  and  drowneth 
that  which  is  weighty  and  solid 

"  Another  error  hath  proceeded  from  too 
great  a  reverence,  and  a  kind  of  adoration  of  the 
mind  and  understanding  of  man  ;  by  means 
whereof,  men  have  withdrawn  themselves  too 
much  from  the  contemplation  of  nature,  and  the 
observations  of  experience,  and  have  tumbled 
up  and  down  in  their  own  reason  and  conceits. 
Upon  these  intellect ualists,  which  are  notwith- 
standing commonly  taken  f  >r  the  most  sublime 
and  divine  philosophers,  Heraclitus  gave  a  just 
censure,  saying,  Men  sought  truth  in  their  own 
little  worlds,  and  not  in  the  great  and  com- 
mon world;  for  they  disdain  to  spell,  and  so 
by  degrees  to  read  in  the  volume  of  God's 
works  :  and  contrariwise  by  continual  meditation 
and  agitation  of  wit  do  urge  and  as  it  were  in- 
vocate  their  own  spirits  to  divine  and  give  oracles 
unto  them,  whereby  they  are  deservedly  deluded. 

"  Another  error  that  hath  some  connexion  with 
this  latter  is,  that  men  have  used  to  infect  their 
meditations,  opinions,  and  doctrines,  with  some 
conceits  which  they  have  most  admired,  or  some 
sciences  which  they  have  most  applied;  and  given 
all  things  else  a  tincture  according  to  them,  utter- 
ly untrue  and  improper.  So  hath  Plato  inter- 
mingled his  philosophy  with  theology,  and 
Aristotle  with  logic  ;  and  the  second  school  of 
Plato,  Proclus  and  the  rest,  with  the  mathematics. 
For  these  were  the  arts  which  had  a  kind  of 
primogeniture  with  them  severally.  So  have  the 
alchy mists  made  a  philosophy  put  of  a  few  ex- 


48  OX   AUTHORITIES. 

periments  of  the  furnace  ;  and  Gilbertus  our 
countryman  hath  made  a  philosophy  out  of  the 
observations  of  a  loadstone.  So  Cicero,  when, 
reciting  the  several  opinions  of  the  nature  of  the 
soul,  he  found  a  musician  that  held  the  soul  was 
but  a  harmony,  saith  pleasantly,  Hie  ab  arte  sua 
non  recessit,  etc.  But  of  these  conceits  Aristotle 
speaketh  seriously  and  wisely  when  he  saith,  ftui 
respiciunt  ad  pauca  de  facili  pronunciant. 

"  Another  error  is  an  impatience  of  doubt, 
and  haste  to  assertion  without  due  and  mature 
suspension  of  judgment.  For  the  two  ways  of 
contemplation  are  not  unlike  the  two  ways  of 
action  commonly  spoken  of  by  the  ancients  :  the 
one  plain  and  smooth  in  the  beginning,  and  in 
the  end  impassable  ;  the  other  rough  and  trouble- 
some in  the  entrance,  but  after  a  while  fair  and 
even  :  so  it  is  in  contemplation  ;  if  a  man  will 
begin  with  certainties,  he  shall  end  in  doubts  ; 
but  if  he  will  be  content  to  begin  with  doubts, 
he  shall  end  in  certainties. 

1 '  Another  error  is  in  the  manner  of  the  tra- 
dition and  delivery  of  knowledge,  which  is  for 
the  most  part  magistral  and  peremptory,  and  not 
ingenuous  and  faithful  ;  in  a  sort  as  may  be  soon- 
est believed,  and  not  easiliest  examined.  It  is 
true  that  in  compendious  treatises  for  practice 
that  form  is  not  to  be  disallowed  :  but  in  the 
true  handling  of  knowledge,  men  ought  not  to 
fall  either  on  the  one  side  into  the  vein  of 
Velleius  the  Epicurean,  Nil  tarn  metuens,  quam 
ne  dubitare  aliqua  de  re  videretur  ;  nor  on  the 
other  side  into  Socrates  his  ironical  doubting  of 


OK  AUTHORITIES.  4!) 

all  things ;  but  to  propound  things  sincerely 
with  more  or  less  asseveration,  as  they  stand  in  a 
man's  own  judgment  proved  more  or  less. 

"  Other  errors  there  are  in  the  scope  that  men 
propound  to  themselves,  whereunto  they  bend 
their  endeavours  ;  for  whereas  the  more  constant 
and  devote  kind  of  professors  of  any  science 
ought  to  propound  to  themselves  to  make  some 
additions  to  their  science,  they  convert  their 
labors  to  aspire  to  certain  second  prizes  :  as  to 
be  a  profound  interpreter  or  commenter,  to  be  a 
sharp  champion  or  defender,  to  be  a  methodical 
compounder  or  abridger,  and  so  the  patrimony 
of  knowledge  cometh  to  be  sometimes  improved, 
but  seldom  augmented. 

"  But  the  greatest  error  of  all  the  rest  is  the 
mistaking  or  misplacing  of  the  last  or  furthest 
end  of  knowledge.  For  men  have  entered  into 
a  desire  of  learning  and  knowledge,  sometimes 
upon  a  natural  curiosity  and  inquisitive  appetite  ; 
sometimes  to  entertain  their  minds  with  variety 
and  delight ;  sometimes  for  ornament  and  repu- 
tation ;  and  sometimes  to  enable  them  to  victory 
of  wit  and  contradiction  ;  and  most  times  for 
lucre  and  profession  ;  and  seldom  sincerely  to 
give  a  true  account  of  their  gift  of  reason,  to 
the  benefit  and  use  of  men  :  as  if  there  were 
sought  in  knowledge  a  couch  whereupon  to  rest 
a  searching  and  restless  spirit ;  or  a  terrace  for 
a  wandering  and  variable  mind  to  walk  up  and 
down  with  a  fair  prospect  ;  or  a  tower  of  state, 
for  a  proud  mind  to  raise  itself  upon  ;  or  a  fort 
or  commanding  ground,  for  strife  and  conten- 


50  ON   AUTHORITIES. 

tion  ;  or  a  shop,  for  profit  or  sale  ;  and  not  a 
rich  storehouse  for  the  glory  of  the  Creator  and 
the  relief  of  man's  estate.  But  this  is  that  which 
will  indeed  dignify  and  exalt  knowledge,  if  con- 
templation and  action  may  be  more  nearly  and 
straitly  conjoined  and  united  together  than  they 
have  been  ;  a  conjunction  like  unto  that  of  the 
two  highest  planets,  Saturn,  the  planet  of  rest 
and  contemplation,  and  Jupiter,  the  planet  of 
civil  society  and  action.  Howbeit,  I  do  not  mean, 
when  I  speak  of  use  and  action,  that  end  before- 
mentioned  of  the  applying  of  knowledge  to  lucre 
and  profession;  for  I  am  not  ignorant  how  much 
that  diverteth  and  interrupteth  the  prosecution 
and  advancement  of  knowledge,  like  unto  the 
golden  ball  thrown  before  Atalanta,  which  while 
she  goeth  aside  and  stoopeth  to  take  up,  the 

race  is  hindered. 

"  Neither  is  my  meaning,  as  was  spoken  of 
Socrates,  to  call  philosophy  down  from  heaven 
to  converse  upon  the  earth  ;  that  is,  to  leave 
natural  philosophy  aside,  and  to  apply  knowl- 
edge only  to  manners  and  policy.  But  as  both 
heaven  and  earth  do  conspire  and  contribute  to 
the  use  and  benefit  of  man  ;  so  the  end  ought  to 
be,  from  both  philosophies  to  separate  and  reject 
vain  speculations,  and  whatsoever  is  empty  and 
void,  and  to  preserve  and  augment  whatsoever  is 
solid  and  fruitful."  (Bacon,  Advancement  of 
Learning,  pp.  39-43,  ed.  1868.) 


V. 

KECAPITULATIOK 

35.    This  brief  Introductory  Discussion,  re- 
capitulated, exhibits  the  following  synopsis  : 

I.  PEDAGOGICS  INCLUDES— 

1.  Education, 

2.  Ethics, 

3.  Psychology. 

II.  EDUCATION    KESTS    UPON    MATERIALS    CON- 
TAINED WITHIN— 

1.  Ethics, 

2.  Psychology. 

III.  EDUCATION,  IN  PART,  DEPENDS  UPON — 

1.  Teaching. 

IV.  TEACHING  ASSUMES  A  KNOWLEDGE  OF  THE 

TWO  ELEMENTS — 

1.  The  mind  that  is  to  be  taught—- 

Psychology, 

2.  The  subject-matter  that  is  to  be 

learned,  drawn  from — 

(a)  Ethics, 

(b)  Psychology. 
V.  ON  AUTHORITIES. 


PART    SECOND. 

•^. 

§§  36-57. 

ON  METHOD  IN  GENERAL. 


METHOD,  .        .        .  .        .        .     §§  36-9. 

SYSTEM, §  41. 

ANALYSIS,         .        .        i        .        .        .        .  §  43. 

SEPARATION, §  44. 

SYNTHESIS, §  45. 

DEFINITION,         ....  §  46 

ABSTRACTION, §  47. 

RECONSTRUCTION, §  49. 

GENERALIZATION,    .        .        .        .        .        .  §  50. 

CLASSIFICATION, §  51. 

INDUCTION, .    .  §  52. 

INTERPRETATION, §  53. 

REPETITION, §  54. 

DEDUCTION, §  55. 

MANNER, §  56. 

MODE, §  57. 


ON  METHOD   IN  GENERAL. 

36.  Method   signifies   literally  the  way  to 
seek  after  a  thing.    The  Greek  philosophers  used 
the  word  in  this  general  sense,  which  has  been 
retained  to  the  present.     Although  writers  agree 
substantially  in  assigning  to  the  term  the  notion 
of  way,  a  principle  which  determines  direction, 
or  orderly  arrangement,  yet  the  precise  limita- 
tions of  the  way  are  not  attributed  with  equal 
clearness  and  uniformity.     By  some,  the  term 
implies  the  only  way  in  which  a  thing  can  be 
done.    By  others,  Method  is  the  only  philosophi- 
cal way  of  proceeding  in  an  investigation,  in- 
volving  actually   two    operations,   analysis    and 
synthesis.     Still  others  see  in  the  word  only  a 
particular  way  of  doing  a  given  thing,  which  way 
may  or  may  not  depend  upon  the  individuality 
of  those  who  achieve  the  task.     (See  Appendix 
A,  §  225.) 

37.  Method  in  general  never  has  respect  to 
the  mind  of  the  learner,  but  always  has  reference 
to  the  subject  studied.     It  assumes  intellectual 
activities  and  products.     It  is  simply  the  way  in 
which   the   mental    products   are   utilized    and 
unified  into  science.     This  field  is  that  of  logic. 
"  I  adopt  the  opinion  of  Mr.  Herbert  Spencer, 
that   logic   is   really  an    objective   science,  like 


56  O!N"   METHOD   IK   GENERAL. 

mathematics    or     mechanics. "       (Jevons,   Pri. 
Sci.,  p.  4,  ed.  1877.) 

38.  The  conception  of  Method  resting  upon 
substantial  data  at  either  end  of  the  process,  it 
is  within  the  province  of  the  term  to  speak  of 
methods  of  business,  when  referring  to  this  or 
that  general  way  by  which  business  transactions 
are  accomplished.      (See  Appendix  A,  §  225.) 

39.  "  The  result  has  been  half  a  century  of 
steady  and  unprecedented  material  growth,  ac- 
companied with  corresponding  improvement  in 
the  structure  of  Government,  which  is  probably 
unequalled    to-day  in   the    success  with  which 
scientific  methods  are  made  to  work   through 
popular  forms."    (The Nation,  No.  700,  p.  328, 
November  28,  1878.)  "  In  a  commercial  country, 
which  depends  so  much  on  the  maintenance  of 
credit,  nothing  is  so  important  as  that  the  credit 
should  rest  on  solid  foundations — not  merely  that 
the  bases  of  the  several  transactions  should  be 
secure,  but  that  the  methods  of  business  should 
be   regular,    legitimate,  and   trustworthy.     The 
credit  of  an  individual  and  of  a  bank  depends 
much  more  on  the  known  fact  that  the  business 
done  is  done  in  a  regular  way,   and  with  the 
habitual  observance  of  certain  rules  of  safe  con- 
duct,  than  upon  a  knowledge  of  the  particular 
securities  which  accompany  it.      The  one  fact 
should  be  certified  to  the  public  in  all  possible 
ways,  the  other  is  in  its  nature  private.     (Ibid., 
p.  330.) 

40.  In  any  investigation  three  distinct  elements 
are  presented  to  the  inquirer  :    (1)  The  object- 


ON   METHOD   IN  GENERAL.  57 

matter,  which  is  the  end  of  the  inquiry  ;  (3) 
The  way  in  which  the  activities  of  the  examiner 
move  forth  and  continue,  while  arriving  at  the 
end  ;  (3)  The  state  or  condition  of  the  one  who 
is  putting  forth  the  exertion  to  secure  the  end. 
A  direct  discussion  suggests  these  questions  : 
(1)  Does  Method  regard  immediately  and  solely 
the  object-matter  of  the  investigation,  how  it  is 
finally  left,  or  to  be  left,  by  the  student,  whether  or 
not  it  shall  be  in  an  orderly  arrangement,  as 
of  Classification?  (2)  Or  does  it  regard  only 
the  way  in  which  the  inquiry  proceeds,  as  by  An- 
alysis, Synthesis,  Induction,  Deduction,  Classifi- 
cation, or  Generalization  ?  (3)  Or  does  it  con- 
sider especially  the  way  in  which  the  scholar,  as 
as  a  particular  individual,  carries  on  his  work, 
whether  in  this  or  that  state  of  mind  or  body, 
or  by  means  of  these  or  those  carefully  chosen 
and  utilized  expedients  and  appliances  which  are 
peculiar  to  himself  alone  ? 

That  is,  in  recapitulation  :  (1)  Does  Method 
point  sharply  and  first  to  the  object  investigated, 
in  what  shape,  form,  or  condition  it  shall  be 
left  ?  (2)  Or  does  it  indicate  the  direction,  or 
way  in,  or  over,  which  the  energy  of  the  mind 
moves  in  its  activity  ?  (3)  Or  does  it  judge  the 
characteristics  which  are  the  difference  between 
the  mind  of  the  examiner  and  that  of  other  men  ? 
In  order  to  answer  these  questions,  it  becomes 
necessary  to  attend  to  each  in  turn. 

41.  I.  Consider  the  object-matter  of  study, 
whatever  it  may  be,  as  arithmetic,  botany,  or 
grammar.  The  purposes  of  examining  any  ob- 


58  ON   METHOD   IN   GENERAL. 

ject  are  to  know  it ;  to  apprehend  its  parts,  as 
single  things  ;  to  discover  the  relations  which 
exist  among  those  parts  ;  to  rearrange  its  parts 
and  relations,  if  thereby  the  mind  can  better 
seize,  comprehend,  or  remember  them,  singly 
and  collectively  ;  to  classify  these  parts  into 
some  new  whole,  which  is  the  product  solely  of 
intellectual  activity  called  thought,  reflection,  or 
simply  reason.  The  student  finds  the  object- 
matter  of  his  attention  in  an  apparently  hetero- 
geneous mass  of  disorder  and  confusion — he 
leaves  it  reduced  into  a  congruous  condition — he 
has  been  entirely  unconscious  of  his  own  eccen- 
tricities, or  individuality,  or  expedients,  or  ways 
in  which  his  activities  and  energies  have  pro- 
ceeded, whether  by  this  or  by  that  process  or 
route — he  has  steadfastly  and  daily  kept  his  at- 
tention upon  the  object-matter,  as  to  what  it  is, 
and  how  he  shall  finally  leave  it  adjusted,  part 
to  part,  part  to  the  whole,  and  the  whole  to 
other  parts  and  wholes — himself  and  the  ways 
by  which  his  thought-powers  went  along  in  their 
work  have  dropped  entirely  out  of  consideration. 
In  this  case  the  idea  of  searching  out  is  not 
found,  because  the  attention  rests  exclusively 
upon  the  object-matter  which  incited  and  de- 
termined the  action  called  seeking  after — that 
is,  the  student  considers  the  purposes  attained, 
and  not  the  routes  or  ways  through  or  by  which 
his  powers  brought  forth  those  classified  and 
organized  ends.  It  follows,  hence,  that  this  is 
not  a  case  of  Method.  The  result  or  end  spoken 


ON  METHOD   IN   GENERAL.  59 

of  is  properly  a  system,  economy,  or  constitu- 
tion.    (See  §  124,  and  Appendix  B,  §  226.) 

42.  II.  Consider  exclusively  tlie  ways  over 
which  the  activities  of  the  intellect  proceed  when 
they  are  engaged  in  an  investigation.   These  may 
be  called  Modes  of  Method  in  General. 

43.  («)  The  faculties  of  observation  are  on 
the  alert  to  discriminate  the  parts  of  the  wholes 
of  the  object -matter  of  investigation,  and  the  at- 
tributes or  characteristics  of  those  parts  or  wholes 
— these  parts  and  attributes  are  likewise  observed 
under  the  light  of  thought  or  reflection,  called 
comparison,  by  which  the  analogous  elements  of 
similars  are  discovered.     This  way,  by  which  the 
powers  of  the  mind  must  pass  in  order  to  discover 
the  individual  Facts,  known  as  elements,  for  the 
relations  called  similars  and  dissimilars,  is  prop- 
erly denominated  Analysis.      (See  Appendix  C, 
§  227.) 

44.  A  rigid  distinction  should  be  observed 
between  analysis  and  separation,  or  division. 
Separation  sets  apart  one  thing  from  another — the 
thing  set  aside  may  be  a  part  of  that  from  which 
it  is  now  placed,  or  it  may  be  some  other  whole 
thing  placed  apart  from  the  former.     Division 
implies  a  taking  asunder,  and  ordinarily  refers 
to  some  whole  which  is  cut  into  parts.     In  separa- 
tion or  division  the  process  ends  with  the  action, 
while  in  analysis  these  parts  are  not  only  made  or 
found,  but  they  are  examined  for  the  purpose  of 
discovering  similarities.  Separation  and  division, 
having  set  apart  the  portions,  give  them  no  farther 
examination   nor  attention.     An  artisan  takes  a 


60  ON   METHOD   IN   GENERAL. 

watch  into  its  parts  for  the  purpose  of  cleaning 
and  repairing  the  time-piece.  His  examination  of 
each  part  is  to  the  sole  end  of  discovering  whatever 
particles  of  dust  may  be  adhering  to  it.  There  is 
no  examination  in  the  interests  of  science  or 
higher  truth,  either  theoretical  or  practical.  This 
is  a  case  of  separation,  rather  than  of  analysis. 

46.  (&)  Assuming  the  foregoing  analysis  com- 
plete, the  powers  of  thought  apprehend  the 
elements,  which  are  to  constitute  the  similars, 
and  from  them  create  a  new  intellectual  product. 
In  this  process  the  unassirnilative  elements  are 
rejected  by  the  mind,  and  form  no  portion  of  the 
new  products.  The  way  or  route  by  which  the 
mind  proceeds  in  creating  these  intellectual  pro- 
ducts is  called  Synthesis.  (See  Appendix  D, 
§228.) 

46.  Sometimes    the  elements  of  a  synthesis 
are  the  products  of  Definition.     (See  Appendix 
E,  §  229.) 

47.  The  process  of    assorting  and  rejecting 
the  analytical  elements  is  known  as  Abstraction. 
(See  Appendix  F,  §  230.) 

48.  "  Analysis  and  synthesis,  though  com- 
monly treated  as  two  different  methods,  are,  if 
properly  understood,    only  the    two    necessary 
parts  of  the  same  method.     Each  is  the  relative 
and  the  correlative  of  the  other.    Analysis,  with- 
out a  subsequent  synthesis,  is  incomplete  ;  it  is 
a  mean  cut  off  from  its  end.     Synthesis,  without 
a  previous  analysis,   is  baseless  ;    for  synthesis 
receives  from  analysis  the  elements  which  it  re- 


ON   METHOD   IK   GENERAL.  61 

composes."     (Sir   W.   Hamilton,   Metaphysics, 
p.  69,  ed.  1871,  Boston.) 

49.  Synthesis  should  be  discriminated  from 
Reconstruction — it  is  Construction,      Recon- 
struction is  the  opposite  of  separation  or  division  ; 
it  simply  re-makes  the  whole  by  re-adjusting  those 
elements  or  parts  which  were  set  aside  from  each 
other — it  fashions  no  new  whole.     Synthesis  is 
Construction  ;  it  fabricates  an  original  product 
which   essentially  and  materially  differs  in  its 
nature  from  any  and  all  of  the  wholes  that  were 
separated  by  analysis.    In  the  supposition  of  the 
watch  (§  44),  if  the  parts  be  restored  to  their 
former  position,  and  the  watch  ' '  put  together  ' ' 
again,  it  is  a  case  of  reconstruction,  rather  than 
of  synthesis.     There  is  no  new  product  created 
by  the  procedure. 

50.  (c)  Analogous  elements  being    assumed 
in  the  possession  of  the  student,  he  proceeds  by 
synthesis   to   "  comprehend,   under   a   common 
name,   several  objects  agreeing   in  some   point 
which  he  abstracts  from  each  of  them,  and  which 
that  common  name  serves  to  indicate. "     This 
way  of  proceeding  is  usually  known  under  the 
name   of   Generalization.     (See   Appendix    G, 

§  231-) 

51.  (d)  Generalization,  in   its  ways   of  pro- 
ceeding, is  but  another  name  for  classification, 
although  in  the  extent  to  which  they  are  carried 
in  science  classification  is  the  more  comprehen- 
sive term.     By  some  writers,  generalization  is 
used  in  reference  to  the  object-matter  of  cause 
and  effect,  while  investigation  proceeding  on  the 


62  ON   METHOD   IN   GENERAL. 

idea  of  observed  resemblances,  is  the  province  of 
Classification.     (See  Appendix  H,  §  232.) 

52.  (e)  When  generalization  or  classification 
is  complete  in   extension  at  any  point   in    the 
ascending  degrees,  and  the  scholar,  by  his  powers 
of  thought,  extends  the  generalization  by  infer- 
ence so  as  to  include  objects  which  the  preced- 
ing generalization  does  not  cover  in  his  experience 
or  observation — thus   making   a   new    creation, 
known  as  a  universal,  sometimes  as  a  general — 
the  product  is  called  an  Induction,     (See  Ap- 
pendix /,  §  233.) 

53.  Induction  should  not  be  confounded  with 
pure  explanation,  or  what  is  known  as  Mathe- 
matical Interpretation.    Induction  creates  a 
new  inferential  product,  the  elements  of  which  are 
discovered  only  by  the  examination  of  many  ob- 
jects, and  the  inference  extends  over  unexamined 
and  unexplored  territory.     Interpretation  places 
itself  at  the   point  of    completion  of   a   single 
observation,  operation,  or   process,  and  retraces 
the  steps  over  the  way  followed,   and  explains 
fully  the  meaning,   extensive  and  intensive,   of 
what  is  observed,  predicting  simply  that  all  similar 
examples  will  be  traced  along  the  same  way,  and 
the  same  ends  reached.     Sciences  founded  upon 
general  definitions  instead  of  observation  and  ex- 
periment, are  not  inductive.    The  Pure  Mathe- 
matical sciences  are  not  properly  inductive,  and 
from  their  nature  cannot  be.     What  is  usually 
called  Mathematical  Induction  is  Interpretation. 
The  so-called  Perfect  Induction  is  hardly  Induc- 
tion in  its  nature,  because  no  product  is  created 


ON   METHOD   IN   GENERAL.  63 

beyond  a  generalization,  or  classification,  and 
nothing  is  gained  by  using  two  terms  for  the 
same  thing,  when  there  are  two  notions  to  be 
distinguished  from  each  other.  (See  Appendix 
/,  §  233,  Nos.  4,  5,  and  7.  Also  Appendix  Jy 

§  234-) 

54.  Another  point  should  be  clearly  outlined  : 
The  mere  Repetition  of  examples,  substantially 
identical,  does  not  increase  the  force  and  certi- 
tude, nor  extend  the  range,  of  an  inference.    One 
example  covers  the  whole  territory,  and  it,  to- 
gether with  all  others  of  the  kind,  does  no  more 
than  illustrate  the  original  principle  established 
directly  or  indirectly  by   definition.     In  arith- 
metic, for  example,  repetition  of  examples  adds 
nothing  to  the  elements  of  which  the   "  rule" 
is  made — it  simply  serves  to  impress  the  way, 
the  procedure,  upon  the  mind  of  a  learner,  simi- 
larly to   the   repetition  in  the  finger    exercises 
upon  the  piano.     (See  §§  204-7.) 

It  should  be  observed  that  there  is  a  great 
variety  of  opinions  among  authors  concerning  the 
nature  of  Induction.  The  citations  in  the  Ap- 
pendix exhibit  some  of  the  views. 

55.  (/)  If  a  scholar  assume  the  possession  of 
generals  or  uni\rersals,   furnished  either  by  In- 
duction, by  Definition,  or  by  Intuition,  and  then 
use  them  with  which  to  compare  individual  facts 
or  truths,  and  by  this  means  establish  individual 
truths  of  like  kind  as  an  end  of  the  process,  the 
way  of  proceeding  is  known  as  Deduction.     (See 
Appendix  K,  §  235.) 

56.  III.    Consider   the    way    in    which    the 


64  ON   METHOD   IK   GENERAL. 

individual  student  addresses  himself  to  his  tasks. 
He  may  be  proceeding  by  any  of  the  above- 
named  modes,  or  ways,  usually  called  Methods, 
and  his  own  characteristics  of  disposition,  habits, 
eccentricities,  may  be  prominent.  These  may  or 
may  not  be  aids  in  securing  valuable  results  of 
his  labors.  In  any  case,  these  are  simply  and 
solely  individualities — they  belong  exclusively  to 
the  investigator — they  are  no  necessary  part  of 
the  mode  or  Method  he  is  following — they  are 
his  Manner. 

Critical  discrimination  should  be  made  be- 
tween what  is  necessary  to  a  way,  and  what  is 
purely  incidental  to  the  individual  who  is  pro- 
ceeding over  that  way.  Indifference  to  this 
discrimination  is  followed  by  the  pedantic  asser- 
tion that  each  man  can  have  a  method  of  his 
own.  Methods  are  ways  which  are  independent 
of  this  or  that  man,  and  which  are  determined 
by  the  nature  of  the  mind  of  man,  or  by  the 
nature  of  the  object-matter  to  be  investigated. 
But  Manner  is  his  individuality  when  proceeding 
in  a  Method.  (See  §  123.) 

57.  When  one's  Manner  is  well  ordered  in  its 
System,  it  is  designated  by  the  term  Mode.  (See 
§  123.) 


PART    THIRD. 


58-216. 


ON  METHODS  OP  TEACHING. 


I.  ON  THE   THEORY  OF  METHODS 
OF  TEACHING,  . 

II.  ON  THE  PRACTICE  OF  METHODS 
OF  TEACHING,  .... 

(A)  On   the    Knowing  Faculties 
of  the  Mind,     .... 

(B)  On  the    Nature  of  Subject- 
Matter,      

(C)  On  Discovering  Methods  of 
Teaching  Special  Subjects, 

III.  CONCLUDING  REFLECTIONS, 


§§  58-143 
§§  144-216 
§§  144-187 
§§  188-210 

§§  211-216 
S§  217-224 


I. 


ON  THE  THEORY  OF  METHODS  OF 
TEACHING. 

58.  "  I  am  afraid  it  must  be  allowed,  that  no 
art,  of  equal  importance  to  mankind,  has  been 
so  little  investigated  scientifically  as  the  art  of 
teaching.  •  No  art  is  in  the  hands  of  practition- 
ers who  are  so  apt  to  follow  so  blindly  in  the  old 
paths.  I  say  this  with  the  full  recollection  that 
there  has  been  great  improvement  in  England 
lately,  and  that  the  books  of  teaching,  most  in 
use,  have  been  purged  of  many  gross  errors  both 
of  statement  and  of  method.  But  one  line  of 
enquiry  there  is  which  has  never  been  sufficiently 
followed,  though  one  would  have  thought  it  ante- 
cedently the  most  promising  of  all, — the  study  of 
the  human  mind  through  actual  observation,  and 
the  study  of  the  expedients  by  which  its  capacity 
for  receiving  and  retaining  knowledge  may  be  en- 
larged. The  field  of  investigation  has  been  al- 
most wholly  neglected,  and  therefore  it  may  just 
be  that  we  are  on  the  eve  of  great  discoveries  in 
education,  and  that  the  processes  of  these  teach- 
ers are  only  a  rough  anticipation  of  the  future. 
The  fact  that  the  methods  of  teaching  follow- 
ed in  England  are  almost  wholly  empirical,  that 


68  ON   THE   THEORY    OF 

for  the  most  part  they  entirely  neglect  individual 
differences  of  character  and  temperament,  that 
they  certainly  work  counter  to  the  known  laws 
according  to  which  some  of  the  mental  faculties 
operate, — for  example;  the  memory — all  these 
facts  seem  to  my  mina  to  point  at  possibilities 
and  chances  of  improvement,  which  a  few 
persons,  by  expedients  which,  I  frankly  allow, 
seem  even  to  me  somewhat  ignoble,  have  perhaps 
had  the  good  fortune  to  realize  beforehand." 
(Maine,  Village  Communities  and  Miscellanies, 
ed.  1876,  pp.  285,  286.) 

59.  A  complete  discussion  of  the  Theory  of 
Methods  of  Teaching  would  include  a  full  inves- 
tigation of  Psychology  and  of  the  nature  of  sub- 
ject-matter to  be  taught — it  would  be  an  exhaus- 
tive examination  of  the  relations  which  exist  be- 
tween the  various  faculties  of  the  mind  and  the 
many  kinds  of  objects  to  be  learned.     It  would 
inquire,  first,  how  mind  acts  as  an  original  cause 
of  activity,  then  what  are  the  nature  and  char- 
acter of  its  capacities,  and  lastly  what  are  the 
products  of  its  activity.      This  investigation  is 
purely  psychological,   and   lies   anterior   to  the 
province  of  logic — it  is  supra-logical,  and  regards 
the  function,  nature,  and  character  of  the  activi- 
ties and  faculties  of  the  mind  that  learns,  and 
that  grows  by  introsusception. 

60.  By  the  nature  of  a  faculty  is  meant  not 
only  its  function,  but  that  native  endowment  of 
its  Potentiality  out  of  which  grow  all  those  suc- 
cessive degrees  of  power  that  manifest  themselves 
in  a  reality. 


METHODS   OF  TEACHING.  69 

61.  By  the  character  of  a  faculty  is  designat- 
ed the  state  in  which  it  exists  at  any  specified 
stage  in  its  growth. 

62.  By  Psychology  is  meant  the  introspective 
study  of  the  experience  of  the  mind  itself. 

63.  "  No   student  of  Locke  and  Hume  can 
read  the  psychological  works  of  the  present  day 
without  feeling  anxiety  for  the  future  of  the  study 
of  Mind  or  Experience.     The  modern  psycholo- 
gist is  profoundly  dissatisfied  with  his  subject ; 
the  exact  and  the  classificatory  sciences,  by  the 
brilliance  of  their  methods  and  results,  fill  him 
with  envy  ;  he  is  painfully  conscious  that  mental 
phenomena  are  not  definite  enough  to  be  the  ob- 
jects of  a  science  ;   he  must  therefore  connect 
them  with  other  phenomena  which  are.     Hence 
the  i  Physiological  Psychology  '  of  our  day.  But 
surely  this  is  not  psychology,  or  the  study  of  ex- 
perience, but  physiology.     Let  us  keep  clearly 
before  our  minds  that  psychology  is  the  study 

of  experience Psychology  then,   if  we 

retain   the   word,   is   a   critique,   a   Method,   a 
certain  thoughtful  attitude  in  science,  morals,  and 
literature.     It  is  the  critical  examination  of  my 
own  adult  opinions,  desires  and  tastes  in  rela- 
tion to  present  objects No  amount 

of  information  respecting  the  evolution  of  belief 
or  sentiment,  and  no  amount  of  mental  physiol- 
ogy can  ever  take  the  place  of  acquaintance  with 
my  own  real  opinions  and  desires.   Modern  works- 
on    mental   science,   with  very  few  exceptions, 
forget   this.     The   conditions  of   ideation,   the 
origin  of  moral  and  aesthetic  feelings,  and  such 


70  ON   THE  THEORY   OF 

like,  are  fully  discussed  ;  but  we  look  in  vain 
for  a  home-question  like  this — i  After  all,  do  t 
really  desire  nothing  for  myself  but  Happiness. ' 
Individualism — thoughtful  reference  to  one's 
own  experience — is  indeed  a  rare  quality  now. " 
(Stewart,  Psychology,  in  Mind,  pp.  445-451, 
No.  IV,  October,  1876.) 

64.  Methods   of    Teaching,    having   an    ac- 
quaintance with   Mind,  consider   the  nature  of 
intellectual  products,  show  in  what  order  they 
follow  each  other,  reveal  the  way  in  which  the 
activities  of  Mind  proceed  with  these  products, 
classify  them,  and  build  up  Science  out  of  them. 
This  is  the  arena  of  Logic,  and  has  reference  to 
System,  or  subject-matter  as  such — it  is  infrar 
psychological.  Succeeding  this  comes  a  thorough 
discussion  of  subject-matter  that  is  to  be  learned 
by  the  mind  of  the  student.     A  treatment  so 
elaborate  could  not  be  concluded  in  one  brief 
Study,  were  it  desirable  to  attempt  it.    Another 
occasion  must  serve  portions  of  this  work,  as  it 
may  occur.     No  more  will  be  essayed  at  this 
time  than  to  survey  the  line  of  the  investigation 
as  well  as  may  be,  by  "  blazing"  the  way,  some- 
times l '  doubling  upon  the  track, ' '  so  that  others 
may  follow  and  clear  up  the  obscurities  and  re- 
move the    errors,   that   lie   upon  this   intricate 
way,  and  enlarge  the  practical  value  which  must 
result  from  a  scientific  research. 

65.  "  Since  the  human  mind  must  conscious- 
ly reproduce  what   actually  exists,  the   act   of 
knowing  is  conditioned  in  two  ways :  a.  Sub- 
jectively, by  the  essence  and  natural  laws  of  the 


METHODS   OF  TEACHING.  71 

human  mind,  especially  by  those  of  the  human 
powers  of  knowledge  ;  b.  Objectively,  by  the 
nature  of  what  is  to  be  known.  The  constitu- 
tions and  relations  of  what  is  to  be  known,  so  far 
as  these  require  different  ways  of  representation 
in  the  act  of  knowing,  we  call  forms  of  existence 
(e.g.,  subsistence  and  inherence).  The  notions 
of  these  forms  of  existence  are  the  metaphysical 
categories.  The  different  ways,  corresponding 
to  these  forms  of  existence,  in  which  what  actual- 
ly exists  is  taken  hold  of  and  copied  in  the  act 
of  knowledge,  are  the  forms  of  knowledge  (e.g., 
the  categorical  judgment).  The  actual  copy,  the 
result  of  the  activity  of  knowledge,  is  the  con- 
tent of  knowledge.  .  .  .  The  laws  of 
knowing,  as  such,  determine  only  the  ways  of 
representation  (copying),  or  the  forms  of  knowl- 
edge, not  its  contents.  .  .  .  These  forms 
of  knowledge  correspond  to  the  forms  of  exist- 
ence, and  they  are  conditioned  by  the  objective 
reality."  (Ueberweg,  Log.  Doct.,  pp.  3,  4,  ed. 
1871.) 

66.  "  The  sense  attached  at  the  present  day 
to  the  words  form  and  matter,  is  somewhat  dif- 
ferent from,  though  closely  related  to,  these 
(form  and  law).  The  form  is  what  the  mind 
impresses  upon  its  perceptions  of  objects,  which 
are  the  matter ;  form  therefore  means  mode  of 
viewing  objects  that  are  presented  to  the  mind. 
When  the  attention  is  directed  to  any  object, 
we  do  not  see  the  object  itself,  but  contemplate 
it  in  the  light  of  our  own  prior  conceptions.  A 
rich  man,  for  example,  is  regarded  by  the  poor 


72  ON   THE   THEORY   OF 

and  ignorant  under  the  form  of  a  very  fortunate 
person,  able  to  purchase  luxuries  which  are 
above  their  own  reach  ;  by  the  religious  mind 
under  the  form  of  a  person  with  more  than  or- 
dinary temptations  to  contend  with  ;  by  the 
political  economist,  under  that  of  an  example  of 
the  unequal  distribution  of  wealth  ;  by  the  trades- 
man, under  that  of  one  whose  patronage  is 
valuable.  Now,  the  object  is  really  the  same  to 
-all  these  observers  ;  the  same  rich  man  has  been 
represented  under  all  the  different  forms.  And 
the  reason  that  the  observers  are  able  to  find 
many  in  one,  is  that  they  connect  him  severally 
with  their  own  prior  conceptions.  The  form, 
then,  in  this  view,  is  mode  of  knowing ;  and 
the  matter  is  the  perception,  or  object,  we  have 
to  know."  (Thompson,  Outline  of  Laws  of 
Thought,  p.  34,  2d  ed.) 

67.  "  Form  is  something  which  may  remain 
uniform  and  unaltered,  while  the  matter  thrown 
into  that  form  may  be  varied.     Medals  struck 
from  the  same  dies  have  exactly  the  same  form, 
but  they  may  be  of  various  matter,  as  bronze, 
copper,  gold,  or  silver.     A  building  of  exactly 
the  same  form  might  be  constructed  either  of 
stone   or   bricks  ;    furniture    of   exactly  similar 
shape  may  be  made  of  oak,  mahogany,   walnut 
wood,  etc."     (Jevons,  El.  Les.  Logic,  ed.  1878, 
pp.  4-5.) 

68.  "Distinction  between  Form  and  Mat- 
ter.— This  phraseology  was  introduced  by  Aris- 
totle, who  represented  every  thing  as  having  in 
itself   both  matter   and    form.     It   had  a    new 


METHODS   OF   TEACHING.  73 

signification  given  to  it  by  Kant,  who  supposes 
that  the  mind  supplies  from  its  own  furniture  a 
form  to  impose  on  the  matter  presented  from  with- 
out. The  form  corresponds  to  the  a  priori  ele- 
ment, and  the  matter  to  the  a  posteriori.  But 
the  view  thus  given  of  the  relation  in  which  the 
knowing  mind  stands  to  the  known  object  is 
altogether  a  mistaken  one.  It  supposes  that  the 
mind  in  cognition  adds  an  element  from  its  own 
resources,  whereas  it  is  simply  so  constituted  as 
to  know  what  is  in  the  object.  This  doctrine 
needs  only  to  be  carried  out  consequentially  to  sap 
the  foundations  of  all  knowledge, — for  if  the 
mind  may  contribute  from  its  own  stores  one 
element,  why  not  another  ?  Why  not  all  the 
elements  ?  In  fact,  Kant  did,  by  this  distinction, 
open  the  way  to  all  those  later  speculations 
which  represent  the  whole  universe  of  being  as 
an  ideal  construction.  There  can,  I  think,  be 
no  impropriety  in  speaking  of  the  original  prin- 
ciples of  the  mind  as  forms  or  rules,  but  they 
are  forms  merely,  as  are  the  rules  of  grammar, 
which  do  not  add  any  thing  to  correct  speaking 
and  writing,  but  are  merely  the  expression  of  the 
laws  which  they  follow.  As  to  the  word  i  mat- 
ter, '  it  has  either  no  meaning  in  such  an  appli- 
cation, or  a  meaning  of  a  misleading  character. ' ' 
(McCosh,  Int.  of  Mind,  p.  312,  ed.  1870.) 

69.  "  The  drift  and  meaning  of  a  branch  of 
knowledge  varies  with  the  company  in  which  it 
is  introduced  to  the  student.  If  his  reading  is 
confined  simply  to  one  subject,  however  such 
division  of  labor  may  favor  the  advancement  of  a 


74  OK   THE   THEORY   OF 

particular  pursuit,  a  point  into  which  I  do  not  here 
enter,  certainly  it  has  a  tendency  to  contract  his 
mind.  If  it  is  incorporated  with  others,  it  de- 
pends on  these  others  as  to  the  kind  of  influnce 
which  it  exerts  upon  him.  Thus  the  Classics, 
which  in  England  are  the  means  of  refining  the 
taste,  have  in  France  subserved  the  spread  of  re- 
volutionary and  deistical  doctrines.  In  Meta- 
physics, again,  Butler's  Analogy  of  Religion, 
which  has  had  so  much  to  do  with  the  conversion 
to  the  Catholic  faith  of  members  of  the  Univer- 
sity of  Oxford,  appeared  to  Pitt  and  others,  who 
had  received  a  different  training,  to  operate  only 
in  the  direction  of  infidelity.  .  .  It  is  not  so 
much  this  study  or  that,  as  it  is  the  setting  into 
other  studies  that  moulds  the  impression.  In 
this  is  the  notion  of  being  liberally  educated — 
that  any  subject  is  received  without  prejudice. ' ' 
(Newman,  Idea  of  A  University,  p.  100,  ed. 
1873.) 

70.  "  The  policy  of  the  present  Minister  of 
Public  Instruction  (Russia)  has  been  to  discoun- 
tenance the  study  of  natural  science,  as  the  source 
of  mutiny  and  insubordination,  and  encourage 
that  of  the  classics,  as  favorable  to  discipline 
and  authority  and  to  the  state  of  religion." 
(The  Nation*^.  704,  Dec.  26,  1878,  p.  393.) 

"  The  generality  of  travellers  enveloped  for- 
ever in  customs,  habits,  prejudices,  and  wants 
peculiar  to  themselves,  move,  as  it  were,  in  an 
atmosphere  of  their  own,  which  divides  them 
from  the  places  through  which  they  pass,  as  from 
so  many  different  worlds.  A  Frenchman  would 


METHODS   OF   TEACHING.  75 

fain  carry  all  France  along  with  him  ;  as  soon  as 
he  misses  the  smallest  of  his  accustomed  con- 
veniences, he  overlooks  its  equivalent,  and  be- 
lieves himself  lost.  Comparing  continually 
what  he  sees  with  what  he  has  quitted,  he  thinks 
it  worse  only  because  it  is  not  the  same,  and 
cannot  sleep  in  the  Indies  if  his  bed  is  not  made 
as  it  was  at  Paris. ' '  (Rousseau,  Emilius,  vol.  iv. , 
pp.  226-7.) 

71.  ff  Knoivledge  is  a  general  term  which  im- 
plies the  thing  known:  science,  learning,  and 
erudition,  are  modes  of  knowledge  qualified  by 
some  collateral   idea  :   science  is  a  systematick 
species  of  knowledge  which  consists  of  rule  and 

.  order  ;  learning  is  that  species  of  knowledge 
which  one  derives  from  schools,  or  through  the 
medium  of  personal  instruction  ;  erudition  is 
scholastick  knowledge  obtained  by  profound  re- 
search ;  knowledge  admits  of  every  possible  de- 
gree, and  is  expressly  opposed  to  ignorance  ;  sci- 
ence, learning,  and  erudition,  are  positively  high 

degrees  of  knowledge Learnin  g  is 

less  dependent  on  the  genius,  than  on  the  will  of 
the  individual  ;  men  of  moderate  talents  have 
overcome  the  deficiencies  of  nature,  by  labour  and 
perseverance,  and  have  acquired  such  stores  of 
learning  as  have  raised  them  to  a  respectable 
station  in  the  republick  of  letters.  Profound  eru- 
dition is  obtained  but  by  few  ;  a  retentive  mem- 
ory, patient  industry,  and  deep  penetration,  are 
requisites  for  one  who  aspires  to  the  title  of  an 
erudite  man. "  (Crabb,  Synonyms.} 

72.  All  knowledge  that  we  possess  must  be 


76  ON   THE   THEORY   OF 

in  some  form — it  would  be  well  to  say  shape,  if 
intellectual  products  or  impressions  could  have 
shape.  The  term  knowledge  is  sometimes  used 
in  two  meanings  :  as  completed  thought,  which 
is  a  product  ;  and  as  the  action  of  the  mind,  the 
completion  of  which  is  a  product.  There  is 
greater  philosophical  precision  if  the  term  be 
assigned  only  one  signification — that  of  the 
noun,  act  or  product.  "  Knowledge  in  its  ex- 
actest  definition  is,  in  its  positive  form,  A  Con- 
scious identification  of  Attribute  with  its  sub- 
ject, as  in  the  affirmative  proposition,  the  sun  is 
bright.  In  its  negative  form,  it  is  A  Conscious 
differencing  of  an  Attribute  from  its  subject, 
as  in  the  negative  proposition,  the  sun  is  not 
dark."  (Day,  Outl.  Ontolog.  Science,  p.  32,  ed. 
1878.) 

73.  "  Knowledge  is  the  act  or  product  of  a 
rational  nature.     As  such  it  ever  tends  to  a  sys- 
tem   which    is    characterized     by    singleness    of 
source  and  aim  ;  and  this  tendency  is  along  the 
line   which    reason    prescribes   to    a   movement 
from  a  recognized  source  to  the  proposed  end. 
There  are  different  specific  sources,  as  there  are 
manifold  specific  aims  in  knowledge,  indeed  ;  but 
reason  is  one  and  its  field  is  one  and  its  aim 
one,  comprehensive  of  all  special  objects  and  all 
special  aims.     There  is  such  a  thing,  therefore, 
as  a  method  in   all  true   rational  knowledge.7' 
(Ibid.,  p.  31.) 

74.  In  these  three  distinct  things — the  source, 
the  end,  and  the  ivay  of  knowledge — the  last  is 
the  method  of  knowledge.  "  The  aim  of  knowl- 


METHODS   OF  TEACHING.  77 

edge  is  Truth.  Knowledge  arrived  at  the  cer- 
tainty of  truth  i&  Science.  Material  (or  real) 
truth  must  be  distinguished  from  (formal)  cor- 
rectness. Material  truth  in  the  absolute  sense, 
or  simply  truth,  is  the  agreement  of  the  content 
(attributes)  of  knowledge  with  what  actually 
exists.  Material  truth  in  the  relative  sense,  or 
phenomenal  truth,  is  the  agreement  of  the  me- 
diately acquired  content  of  thought  with  the  im- 
mediate outer  or  inner  perceptions  which  exist 
when  the  soundness  of  the  mind  and  of  the 
bodily  organs  is  undisturbed,  or  would  exist 
under  the  corresponding  outer  conditions." 
{Ueberweg,  Logical  Doct.,  pp.  5,  6,  ed.  1871.) 

75.  All  these  illustrations  of  the  province  of 
knowledge  compel  attention  to  the  stages  of  the 
process  of  acquiring  knowledge  by  the  mind  of 
the   learner.      (1)    There   is  the  source    of   the 
activity  residing   in   the    innate    power  of   the 
mind  to  act  responsively  and  intuitively  at  the 
presence    of    objects  to  be    known.      This  in- 
nate power  of  the  mind  is  called  the  ultimate 
€ause  of  Knowledge,  or  simply  the  Cause.     (2) 
There  is  the  rational  way  in  which  this  activity 
proceeds,  usually  at  the  dictation  of  the  power 
of  the  Will.     This  way  is  known  as  the  Method 
of  Thought.     (3)  There  is,  lastly,  the  end  of  the 
activity.     This  consummation  of  the  process  into 
completeness  is  known  as  the  act,  or  product  of 
knowledge,  or  simply  Knowledge. 

76.  The  preceding  discussion  relates,  in  the 
most   general    sense,    to    the   consideration    of 
knowledge  as  acquired   by  the  learner.     In  or- 


78  OST  THE  THEORY   OF 

dinary  acceptance  the  notion  of  learning  is  as- 
sociated with  two  persons — the  one  an  instruc- 
tor or  teacher  of  the  other,  who  is  called  the 
learner,  student,  scholar,  child,  or  pupil.  When 
the  pupil  learns  through  the  instrumentality  of  a 
living  teacher  he  is  said  to  be  taught. 

77.  When  he  learns  without  this  instrumen- 
tality, he  is  said  to  be  self -informed,  or  self- 
educated.  The  self-informed  student  applies 
himself  to  understand  whatever  engages  his  atten- 
tion, whether  books,  or  objects  of  nature,  or  works 
of  art ;  he  applies  his  powers  of  observation  and 
of  reason  to  the  things  that  he  finds  scattered 
about  him  as  a  heterogeneous  mass  ;  he  constructs 
his  own  questions  for  himself,  invents  his  own 
illustrations,  creates  his  own  hypotheses,  and  ad- 
judges the  validity  of  his  own  arguments  and 
conclusions — that  is,  he  alone  pronounces  upon 
the  form  and  matter  of  his  knowledge,  -  and 
way  of  approaching  it.  In  very  many  impor- 
tant matters  he  must  leave  it  for  time  and  experi- 
ence to  inform  him  whether  his  knowledge  is 
correct  in  fact.  The  element  of  time  spent  in 
arriving  at  truth  by  the  self-educated  student  is 
often  great  for  the  amount  and  quality  of  knowl- 
edge gained.  The  difficulties  that  present  them- 
selves to  this  learner  are  frequently  sufficient  to 
deter  any  but  the  most  persevering  and  venture- 
some from  attempting  to  surmount  them.  The 
fields  of  learning  are  so  many  and  so  extensive, 
and  human  life  so  short,  that  the  imperative 
demands  of  our  brief  years  give  a  practical 
value  to  some  kinds  of  knowledge  over  others. 


METHODS   OF  TEACHING.  79 

The  exclusively  self-informed  student  is  not  as- 
sured that  his  learning  is  best  calculated  to  pro- 
mote the  welfare  of  himself  and  his  fellow-man. 
A  well-authenticated  instance,  related  to  the 
writer  by  Dr.  J.  Dorman  Steele,  will  illustrate 
this  statement  :  A  young  man  of  excellent 
parts  entered  college.  He  had  adopted  the 
theory  that  self -education  is  the  only  way  to 
learning,  and  refused  to  consult  or  study  books 
to  prepare  his  lessons.  He  attended  the  recita- 
tions, observed  closely  what  was  said  there,  and 
depended  upon  his  genius,  or  "  inner  conscious- 
ness, "  to  evolve  from  himself  the  knowledge 
he  possessed.  In  process  of  time  he  was  grad- 
uated, and  dropped  into  obscurity.  After  five 
or  six  years  he  suddenly  appeared  at  the  office 
of  the  president  of  the  college.  He  desired  to 
submit  to  the  president  a  law  in  physics  which 
he  had  discovered  by  his  own  unaided  obser- 
vations during  the  past  six  years.  If  approved 
by  the  president,  he  would  publish  his  discov- 
ery. He  had  discovered  "  that  heat  expands 
metals,  and  cold  contracts  them."  The  presi- 
dent called  his  little  daughter,  and  asked  her, 
what  is  the  "  first  law  in  Natural  Philosophy  "? 
She  said,  "  That  heat  expands  metals,  and  cold 
contracts  them."  Said  the  president,  "  You 
see  how  many  valuable  years  you  have  lost  by 
neglecting  to  study  books  as  well  as  objects, 
depending  entirely  upon  your  own  inner  con- 
sciousness for  your  knowledge." 

78.  These  considerations  of  reason  and  ex- 
perience bring  forward  the  idea  of  aiding  the 


80  ON  THE  THEORY   OF 

youth  of  the  State  by  means  of  appropriating 
to  their  benefit  the  learning  and  experience  of 
some  of  the  older  members  of  the  State.  Those 
who  consciously  and  methodically  aid  the  young 
in  acquiring  learning  and  experience  are  known 
as  Teachers.  The  efforts,  which  they  put  forth 
to  advance  their  pupils  in  knowledge,  constitute 
the  idea  that  is  designated  Teaching. 

79.  Teaching  is    consciously   adjusting   ob- 
jects and  acts  to  the  proper  faculties  and  ca- 
pacities of  the  learner.      "Adjust  is  to  set  right 
(Fr.   juste,    straight,    right).     Hence  the  word 
implies  some   relative  order,  shape,  or  standard, 
to  which  matters  have  to  be  brought,  or  some 
antecedent  condition    of    inherent    fitness    to 
which  they  have  to  be  reduced. "    (Smith,  Syn. 
Discr.)     The  order  in  which  objects  are  to  be 
presented  to  the  pupil    is    determined  by  the 
teacher.     Nature,   as  the  child  finds  her,   pre- 
sents objects  to  it  in  an  unclassified,   promis- 
cuous mass.     The  pupil  may  see  a  cat,  then  an 
elephant,  then  a  thunder-storm,  all  in  one  hour. 
The  teacher  would  present  objects  in  a  sequence 
determined  by  previous   study  and  classification. 
This  order  is  artificial  to  the  child,  compared 
to  the  heterogeneous  order  in  which  Nature  ex- 
hibits objects  to  it.     From  this  view,  it  may  be 
said  that  teaching  is  the   conscious  and  philo- 
sophic adjustment  of  object-matter  to  the  abili- 
ties of  the  pupil. 

80.  The  teacher  has  other  duties  towards  his 
pupil.     He   presents   before   the   mind   of   the 
learner  some  entire  object — Nature  also  usually 


METHODS   OF  TEACHING.  81 

does  this,  but  she  leaves  the  mind  to  struggle 
with  the  whole  at  once — the  teacher,  finding  the 
whole  too  vast  for  the  pupil,  separates  it,  prac- 
tically and  virtually,  into  parts.  This  process 
of  dissection  may  be  accomplished  by  using  the 
scalpel,  the  hammer,  or  by  questions  ;  for  ques- 
tions are  but  knives  that  dissect  out  parts  to 
display  to  the  pupil,  or  they  are  colter-shares 
that  cut  out  furrows  in  the  turf,  narrower  or 
wider,  for  the  pupil  to  turn  over,  according  to 
his  strength. 

81.  The  teacher  has  still  other  duties  in  the 
case.     He  is  to  note  both-  the  form  and  the 
matter  of  the  knoivledge  which  the  learner 
acquires,  whether  it  stand  in  his  mind  correct  in 
its  impression  and  true  in  its  essence.     To  se- 
cure these  ends  requires  consummate  skill  of  the 
teacher  :  his  reason  must  be  well  trained   and 
certain  in  its  logical  processes,  his  wit  must  be 
ready  at   analogies,  his  imagination  must  be  fer- 
tile in  illustration,  his  hands  must  be  cunning  in 
constructing,    his  understanding  must   be    pro- 
found, and  his  knowledge  must  be  overflowing 
in  its  quantity.     Here  lie  the  purely  professional 
regions  of  teaching — here  also  are  the  processes 
called  Methods  of  Teaching. 

82.  Tne  teacher  has  now  reached  the  great 
question   of  the   Profession  :    How   to   teach.  ? 
For  it  is  in  teaching  and  with  teachers,  as  it  is 
in  Logic,  "  Where  two  conditions  are  found  or 
assumed  :  Firstly,  that  there  exist  certain  men- 
tal laws  to  which  every  sound  thinker  is  bound 
to  conform.     Secondly,    that  it  is  possible  to 


82  ON   THE   THEOKY   OF 

transgress  those  laws,  or  to  think  unsoundly/' 
(Mansel,  Prolegomena  Logica,  p.  16,  ed.  1860.) 

83.  In   order  to  answer  this  question,  How 
to  teach  ?  even  approximately,    it  is  necessary 
to  enter  into  a  more  critical  examination   of  the 
conception  of  the  word  Teaching.      To  teach 
requires,    obviously  :     (1)    The    mind    of    the 
learner,  or  the  learner  ;  (2)  The  mind   of  the 
instructor,  or  the  teacher  ;  (3)  The   objects,  ac- 
tions, or  things  to  be  learned  by  the  student, 
which  are   commonly    designated,    collectively, 
as  subjects,   subject-matter,   objects,   or  object- 
matter.    The  intellectual  activities  of  the  teacher 
proceed  under  certain  fixed  laws  of  mind.     His 
intellectual  faculties  conform  to  spheres  of  ac- 
tivity into  which  they  are  necessitated  or  deter- 
mined by  their  very  nature.     He  cannot  remem- 
ber with  his  faculty  of  imagination,  nor  reason 
with  memory.     He  must  perceive  with  his  senses, 
reason  with  his  reflective  powers,  and  retain  by 
his  memory.     As  with  the  teacher  so  with  the 
learner,  whose  mental  faculties  and  capabilities 
may  differ  from  those  of  the  teacher  in  original 
quantum  of  functional  endowment,  and  in  de- 
grees of  power,  but  not  in  kind  or  function. 

84.  This  being  true,  the  case  resolves  itself 
into  this  :  (1)  If  the  teacher  knew  subject-mat- 
ter thoroughly  he  could  arrange  its  parts  into 
any  order  of  dependence,  or  steps,  or  points,  or 
classifications,  that  circumstances  or  exigencies 
might  necessitate,  or  expediency  demand.     This 
would  enable  him  to   arrange  and  present  his 
system  of  subject-matter.    (2)  If,  in  addition 


METHODS   OF   TEACHING.  83 

to  tliis,  he  knew  mind  thoroughly,  in  its  facul- 
ties, powers,  capabilities,  laws  of  growth — in 
short,  in  its  nature  and  character,  he  would  know 
exactly  how  to  adjust  the  subject-matter  to  be 
learned  to  the  mind  that  is  to  learn  it. 
Varying  circumstances  of  state  or  condition, would 
not  prevent  this  certainty  of  adj  ustment — it  would 
be  like  the  scientist  adjusting  the  object  that 
he  is  examining  to  the  focus  of  his  microscope 
so  that  his  eye  can  see  it  in  defined  outline. 
(3)  If,  succeeding  these  two  suppositions,  the 
teacher  now  turns  his  attention  for  the  time  ex- 
clusively to  consider  the  ways  in  which  his  sys- 
tem of  subject-matter  shall  be  set  before,  or  in 
the  presence  of,  those  faculties  which  are  the 
native  ones  to  acquire  learning  from  this  sys- 
tem,— if  he  does  this,  he  will  be  carrying  on  in- 
vestigations in  a  province  which  is  original  and 
peculiar  to  the  Profession  of  Teaching. 

86.  A  recapitulation  of  these  points  presents  : 
1)  The  first  field  opened  for  the  teacher-candi- 
"  is  that  of  subject-matter  to  be  taught  by 
him,  and  that  is  to  be  learned  by  the  student. 
This  is  the  region  of  System, — of  scholarship  in 
the  ordinary  branches  of  learning  as  they  are 
found  in  our  schools,  or  as  he  may  analyze  and 
classify  for  presenting  to  his  pupils.  (2)  The 
second  field  for  the  teacher-in-expectancy  is  also 
that  of  subject-matter,  and  is  included  within  the 
range  of  our  schools.  It  is  special,  however,  to 
the  Profession  of  Teaching,  and  is  known  by 
the  name  of  Psychology,  Mental  Philosophy,  or 
Intellectual  Philosophy.  (3)  The  third  field  is 


84  ON  THE   THEORY   OF 

that  of  the  science  and  art  of  adapting  object- 
matter  to  the  capabilities  of  the  mind  to  be 
taught,  that  of  adjusting  objects  to  the  focus 
of  the  intellectual  vision  of  the  pupil. 

86.  This  is  properly  the  Province  of  Meth- 
ods  of  Teaching.     This   province    is   that   of 
Principles — it  is  that  of  those  Principles  which 
exist  in  the  constitution  of  things,  and  according 
to    which    certain    subject-matter   must   be   ac- 
quired by  the  mind  in  a  certain  fixed  way,  pro- 
vided it  ever    becomes    an    actual    knowledge 
within   that    mind.        Some    subject-matter   is 
learned  by  one  faculty,  some  by  another.     In- 
termediate between  every  kind  of  subject-matter 
and  knowledge  of  it,  there  is  the  faculty  which 
is  native  to  the  acquiring  of  that  knowledge. 
If  the  proper  faculty  be  not  approached,  true 
knowledge    cannot  be    the    product — from  this 
conclusion  there  is  no  escape. 

87.  "A  principle  is  that  which  being  derived 
from  nothing,    can    hold  to  nothing. 

What  is  common  to  all  first  principles  is  that 
they  are  the  primary  source  from  which  any 
thing  is,  becomes,  or  is  known."  (Fleming, 
Vocab.  of  Phil.) 

88.  "A  Principle  is  a  central  or  representa- 
tive truth  in  philosophy,  science,  art,   religion, 
or  morals,   which  is  fundamental    and  general, 
and  out  of  which  other  matters  of  a  speculative 
or  practical  character  flow,  and  become  its  prac- 
tical    illustration.      '  He    who    fixes   upon   false 
principles    treads  upon  infirm   ground,  and  so 
sinks  ;  and  he  who  fails  in  his  deductions  from 


METHODS   OF  TEACHING.  85 

right  principles  stumbles  upon  firm  ground , 
and  so  falls. — South."  (Smith,  Syn.  Discr., 
Doctrine. ) 

' t  Principle  carries  knowledge  with  it,  and  is- 
applicable  to  action  as  a  guide  or  basis  of  pro- 
ceeding. A  principle  is  a  fundamental  truth, 
or  comprehensive  law,  from  which  others  are 
derived,  or  on  which  they  are  founded.  It  may 
be  observed,  generally,  that  principles  are  last  in 
the  order  of  investigations,  and  first  in  the  order 
of  practice.  They  are  arrived  at  by  analysis, 
and  when  found  become  bases  or  starting-points- 
for  action  or  scientific  inquiry. "  (Ibid.,  Prov- 
erb.) 

89.  Methods  of  Teaching  are  principle* 
of  adapting  subject-matter  to  the  capaci- 
ties and  powers  of  the  pupil.     When  the 
teacher  says  that  this  subject-matter  should  be 
presented  for  cognizance  by  this  or  that  faculty 
of  the  mind,  and  in  such  and  such  quantities, 
according  to  the  strength  of  those  faculties,  he  is. 
acting  within  the  province  of  Methods  of  Teach- 
ing.    But  when  the  teacher  says  that  this  point 
or  step  of  this  subject-matter  should  succeed  that 
or  that  step  or  point,   he  is  acting  within  the 
scope  of  a  System  of  subject-matter. 

90.  These  two  distinct  operations  are  often 
confounded,    or  used    indiscriminately,    causing 
great  confusion  in  the  proper  use  of  terms.     In 
the  following  the  word  System  is  properly  used  : 
"  The  Gospel  of  St.  John,  adapted  to  the  Ham- 
iltonian  System,  by  an  Analytical  and  Interline- 
ary  Translation  from  the  Italian,  with  full  In- 


86  ON  THE   THEORY   OF 

structions  for  its  use,  even  by  those  who  are 
wholly  ignorant  of  the  language.  For  the  Use 
of  Schools.  By  James  Hamilton,  Author  of  the 
Hamiltonian  System,  London,  1825."  (Sydney 
Smith,  Essays,  p.  74,  late  ed.)  In  the  expres- 
sion, il  Grube's  Method  of  Teaching  Number," 
the  word  Method  is  improperly  used.  It  should 
be  "  Grube's  System,"  because  the  author  ar- 
ranges the  subject-matter  in  such  a  way  that  the 
processes  of  addition,  subtraction,  multiplica- 
tion, and  division,  must  be  taught  in  such  and  such 
a  sequence  of  order,  and  in  such  and  such  an 
order  of  steps.  The  teacher  in  this  case  is  not 
investigating  what  faculties  are  to  be  incited  to 
learn  these  steps,  nor  in  what  quantities  the  sub- 
ject-matter shall  be  set  to  those  faculties,  as 
Methods  require.  The  same  remarks  apply  to 
the  so-called  "  A,  B,  C  Method"  of  teaching 
children  to  read,  the  "  Word  Method,"  and  all 
similar  expressions,  where  Method  is  used  im- 
properly for  System. 

91.  The  questions  relating  to  what  branches 
shall  be  taught  or  studied,  do  not  belong,  in 
strict  analysis,  to  the  Province  of  Methods  of 
Teaching.  They  are  questions  of  Ethics  and 
of  Psychology, — of  the  relations  of  the  individual 
to  the  Family,  the  Society,  and  the  State,  of 
which  he  is  a  member  and  a  part,  according  to 
the  estimate  of  these  relations  by  each  people 
or  nation  for  itself.  They  also  are  within  the 
•field  of  the  development  of  man  as  man,  in  his 
subjective  condition — that  is,  in  his  psychological 
estate.  They  belong  to  the  wider  field  of  Peda- 


METHODS   OF  TEACHING.  87 

gogics,  or  Education,  or  to  what  Mr.  J.  fci.  Mill 
calls  '*  Ethology,  the  science  of  which  education 
is  the  art."  (Chamb.  Encycl.,  article  Educa- 
tion.) 

92.  "  Ethics  may  be  defined  as  the  Science 
of  Practice  or  Conduct  :  the  latter  term  is  pref- 
erable,  as   Practical  Science  is   more   conveni- 
ently used  to  include  along  with  Ethics  the  cog- 
nate studies  of  Jurisprudence  and  Politics. 

' '  All  three  alike  are  distinguished  from  specu- 
lative sciences  by  the  characteristic  that  they 
attempt  to  determine  not  the  actual  but  the 
ideal  :  what  ought  to  exist,  not  what  does  ex- 
ist. An  objection  is  sometimes  taken  to  the  ap- 
plication-of  the  term  '  Science  '  to  such  studies 
as  these.  It  is  said  that  a  Science  must  neces- 
sarily have  some  department  of  actual  existence 
for  its  subject-matter  :  and  there  is  no  doubt  that 
the  term  '  Moral  Sciences  '  is  frequently — per- 
haps more  frequently — used  to  denote  studies  that 
deal  with  the  actually  existent :  viz.  Psychology, 
or  a  portion  of  it  ;  what  Mr.  Mill  calls  Ethology, 
or  the  inquiry  into  the  laws  of  the  formation  of 
character  ;  and  Sociology,  or  (as  it  has  also  been 
termed)  the  Physiology  of  Society. "  (Sidg- 
wick,  The  Methods  of  Ethics,  p.  1,  ed.  1874, 
London.) 

93.  Voluntary  and  conscious  instruction  and 
teaching    are    the  handmaids  of  education,  and 
are   ways  of  approaching  mind,   setting  before 
that  mind  those  branches  of  study  which  Ethics 
and  Psychology  determine  are  best. 

94.  Those  principles  of  Ethics  and  Psychology 


88  ON"   THE   THEORY    OF 

According  to  which  peoples,  families,  or  individ- 
uals, determine  what  branches  of  study  shall  be 
pursued  in  schools  and  elsewhere,  are  properly 
denominated  Methods  of  Pedagogics.  The 
term  Education  being  used  by  English  and  Amer- 
ican authors  as  nearly  or  quite  the  equivalent  of 
the  German  Pedagogics,  Methods  of  Educa- 
tion will  be  used  instead  of  Methods  of  Peda- 
gogics. Methods  of  Education  regard  the  future 
man  as  a  member  of  a  given  society ;  they 
consider  what  the  child  is  to  become ;  they 
are  subjects  of  choice  by  nations,  communities, 
families,  or  individuals,  because  they  determine 
the  uses  to  be  made  of  the  learning  and  disci- 
pline which  nations  or  families  require  of  the 
young.  In  Germany,  Methods  of  Education  are 
determined  by  the  condition  of  the  body-politic, 
and  are  well  established.  In  France,  the  Meth- 
ods of  Education  differ  from  those  of  Germany, 
in  so  far  as  the  purposes  of  the  government  differ 
from  those  in  Germany.  In  England,  Methods 
of  Education  still  vary,  as  also  they  do  in  the 
United  States.  Whatever  purposes  Methods  of 
Education  propose  for  the  young,  they  always 
point  distinctly  to  the  end  that  these  young- 
persons,  when  grown  up,  shall  be  good  and  loyal 
citizens  of  that  Community  or  State.  Methods 
of  education  in  France  are  not  calculated  to  pro- 
duce good  citizens  for  Germany,  but  for  France. 
It  is  the  same  with  every  nation.  Families 
adopt  Methods  of  Education  which  aim  at  giv- 
ing specific  direction  to  the  energies  of  the 
children  in  those  families,  referring  immediately 


METHODS   OF   TEACHING.  89 

to  the  positions  which  these  children  shall  come 
to  occupy,  as  professional,  diplomatic,  or  gov- 
ernmental. These  Methods  inquire  what  is  to 
be  studied  by  the  learner,  in  order  that  he  may 
attain  a  certain  end  desired.  Methods  of  Teach- 
ing are  concerned  in  Methods  of  Education  only 
so  far  as  to  ask  in  what  way  shall  the  branches 
determined  by  the  family  or  the  nation  be  pre- 
sented to  the  mind.  Methods  of  Teaching  know 
no  nationality  nor  family  ;  Methods  of  Education 
preserve  nationality  and  family  attainments.  To 
elaborate  the  subject  of  Methods  of  Education 
would  require  an  extended  treatise,  and  must  be 
set  aside  until  a  more  convenient  time  shall  pre- 
sent itself  for  the  work. 

95.  In  the  following  quotation  the  province 
of  Methods  of  Teaching  is  not  discriminated  from 
that  of  Methods  of  Education,  although  the  no- 
tion of  Method  in  general  is  very  clearly  out- 
lined : 

"  The  Methodick  :— (1)  The  Educator  must 
guide  the  pupil  to  knowledge  of  the  outer 
world  by  aiding  him  to  acquire  it  for  himself  in 
accordance  with  the  natural  operation,  succes- 
sive movements  or  procedure  of  Intelligence  ; — 
that  is  to  say,  according  to  the  way  or  method 
whereby  Intelligence  proceeds  and  must  proceed. 
These  processes,  as  we  have  seen,  are,  in  the  first 
instance,  Analytic,  but  have  Synthesis  and  In- 
duction for  their  end.  When  ascertained,  they 
yield  the  doctrine  of  Method  in  Education — The 
Methodick  of  Education. 

"  (2)  The  Educator  must  perform  the  same 


90  OK  THE  THEORY   OF 

task  with  reference  to  the  higher  feelings  and 
emotions,  with  a  view  to  constitute  them  habit- 
ual motives.  In  things  of  sense  or  of  thought 
the  learner  learns  by  truly  knowing  :  in  things 
of  action  the  learner  learns  through  the  action 
of  others,  and  by  his  own  action.  The  doc- 
trine of  The  Methodick  of  Education  is  to  be 
called  Methodology,  and  embraces  the  applica- 
tion of  Method  to  every  subject  of  intellectual 
study  and  to  every  stage  of  ethical  training 
alike  (page  16).  . 

"  The  way  of  carrying  out  the  Educative 
process  to  a  successful  issue,  both  intellectual 
and  ethical,  is,  as  we  have  seen,  The  Method- 
ick of  Education  (p.  18.)  .  .  .  How  must 
I  convey  instruction  so  as  to  insure  assimilation 
by  the  pupil  ?  .  .  .  The  answer  to  this  ques- 
tion contains  the  Doctrine  of  Method,  and  rests 
on  the  process  of  the  Will  in  its  movements 
towards  knowledge.  Dependent  on  this  are — 
Particular  Methods."  (Laurie,  Synopsis  of 
Lect.,  p.  20,  1877.) 

96.  Methods  of  Education  have  regard  for  the 
growth  of  mind  as  an  end  or  habit  unto  itself, 
an  object  to  be  attained  for  itself,  and  also  for 
knowledge  or  matter,  as  an  end.  (1)  "  What 
subjects  of  instruction  must  I  teach  in  order  to 
give  to  the  future  man  the  materials  of  right 
judgment  ?  (The  Real.)  This  leads  us  into  a 
discussion  of  subjects  of  Instruction  generally 
and  their  relative  values.  (2)  How  must  I  in- 
struct so  as  most  effectually  to  exercise  the  in- 
telligence of  the  pupil  in  making  those  distinc- 


METHODS   OF  TEACHING.  91 

tions  on  which  the  Tightness  of  judgment  de- 
pends ?  (The  Senses.  The  Formal  as  Will-power 
in  reference  to  Intelligence.)  The  answer  to  the 
first  of  these  questions  contains  the  Doctrine  of 
the  Real  with  reference  to  the  outer  world — the 
substance  of  Knowledge.  The  answer  to  the 
second  questions  contains  the  Doctrine  of  Formal 
discipline  in  its  intellectual  relations."  (Laurie, 
Synopsis  of  Led.,  p.  20,  1877.) 

97.  "  It  is  a  physiological  law,  first  pointed 
out  by  M.  Isidore  St.  Hilaire,  and  to  which 
attention  has  been  drawn  by  Mr.  Lewes  in  his 
essay  on  Dwarfs  and  Giants,  that  there  is  an 
antagonism  between  growth  and  development. 
By  growth,  as  used  in  this  antithetical  sense,  is 
to  be  understood  increase  of  size ;  by  develop- 
ment, increase  of  structure.  And  the  law  is, 
that  great  activity  in '  either  of  these  processes 
involves  retardation  or  arrest  of  the  other.  A 
familiar  illustration  is  furnished  by  the  cases  of 
the  caterpillar  and  the  chrysalis.  In  the  cater- 
pillar there  is  extremely  rapid  augmentation  of 
bulk  ;  but  the  structure  is  scarcely  at  all  more 
complex  when  the  caterpillar  is  full-grown  than 
when  it  is  small.  In  the  chrysalis  the  bulk  doe& 
not  increase  ;  on  the  contrary,  weight  is  lost 
during  this  stage  of  the  creature's  life  ;  but  the 
elaboration  of  a  more  complex  structure  goes  on 
with  great  activity.  The  antagonism,  here  so 
clear,  is  less  traceable  in  higher  creatures,  be- 
cause the  two  processes  are  carried  on  together. 
But  we  see  it  pretty  well  illustrated  among  our- 
selves by  contrasting  the  sexes.  A  girl  develops 


92  OX   THE   THEORY   OF 

in  body  and  mind  rapidly,  and  ceases  to  grow 
comparatively  early.  A  boy's  bodily  and  men- 
tal development  is  slower,  and  his  growth 
greater.  At  the  age  when  the  one  is  ma- 
ture, finished,  and  having  all  faculties  in  full 
play,  the  other,  whose  vital  energies  have  been 
more  directed  towards  increase  of  size,  is  rela- 
tively incomplete  in  structure  ;  and  shows  it  in  a 
comparative  awkwardness,  bodily  and  mental. 
Now  this  law  is  true  not  only  of  the  organism  as 
a  whole,  but  of  each  separate  part.  The  abnor- 
mally rapid  advance  of  any  part  in  respect  of 
structure  involves  premature  arrest  of  its  growth  ; 
and  this  happens  with  the  organ  of  the  mind  as 
certainly  as  with  any  other  organ.  The  brain, 
which  during  early  years  is  relatively  large  in 
mass  but  imperfect  in  structure  will,  if  required 
to  perform  its  functions  with  undue  activity, 
undergo  a  structural  advance  greater  than  is  ap- 
propriate to  the  age  ;  but  the  ultimate  effect 
will  be  a  falling  short  of  the  size  and  power  that 
would  else  have  been  attained.  And  this  is  a 
part  cause — probably  the  chief  cause — wrhy  preco- 
cious children,  and  youths  who  up  to  a  certain 
time  were  carrying  all  before  them,  so  often 
stop  short  and  disappoint  the  high  hopes  of  their 
parents."  (Herbert  Spencer,  Education,  pp. 
271,  272,  ed.  1870.) 

"  To  grow  is  the  process  of  which  to  in- 
crease is  the  result  or  manifestation.  Trade  has 
been  growing  for  years  past,  and  is  now  consid- 
erably increased.  To  increase,  however,  does 
not  necessarily  imply  to  grow  ;  rapid  expansion 


METHODS   OF  TEACHING.  93 

or  dilatation  of  parts  will  produce  increase  in 
bulk  ;  but  the  process  of  growth  implies  either 
an  accretion  of  parts  by  external  apposition,  or 
an  assimilative  power  from  within,  as  in  the  vi- 
tal force.  The  snowball  grows  by  accretion, 
and  so  increases  as  it  rolls.  The  tree  grows  by 
its  own  vitality,  and  increases  also  in  size." 
(Smith,  Syn.  Discr.] 

98.  Methods  of  Teaching  consider  the  growth 
of  the  faculties  of  the  mind,  and  the  quantity  of 
knowledge,  not  as  ends,  but  as  necessary  knowl- 
edge from  which  to  project  anew  procedures  in 
teaching  while  the  mind  of  the  learner  is  grow- 
ing. This  is  essential  in  order  that  the  teacher 
may  set  to  this  learner,  at  any  stage  of  his 
growth,  the  maximum  quantity  of  subject-mat- 
ter which  the  present  attainments  and  powers 
of  the  learner  can  master ;  to  set  less  than 
this  amount  to  a  pupil  is  puerile,  and  to  set 
more  is  to  prevent  his  powers  from  compre- 
hending it.  Yet  the  faculties  of  mind  grow  into 
powers  far  more  rapidly  by  attempting  to  com- 
prehend the  unknown,  the  mysterious,  by  trying 
to  enlarge  the  maximum  degrees  of  efforts,  than 
by  resting  contentedly  with  efforts  near  the 
minimum  of  degrees.  "  Mental  dyspepsia'7 
comes  from  starvation,  as  well  as  from  plethora 
of  subject-matter.  "  A  well-regulated  course  of 
study  will  no  more  weaken  the  mind  than  hard 
exercise  will  weaken  the  body  ;  nor  will  a  strong 
understanding  be  weighed  down  by  its  knowl- 
edge, any  more  than  an  oak  is  by  its  leaves,  or 
than  Samson  was  by  his  locks.  He  whose  sinews 


94  .       OST   THE   THEORY   OF 

are  drained  by  his  hair,  must  already  be  a  weak- 
ling." (Grindon,  Life,  p.  197.)  "  If  the  child 
of  eight  years  old  finds  his  improved  language 
understood  by  a  child  of  three,  why  should  you 
contract  yours  to  his  vocabulary  ?  Always  em- 
ploy a  language  some  years  in  advance  of  the 
child  (men  of  genius  in  their  books  speak  to  us 
from  the  vantage-ground  of  centuries)  :  speak  to 
the  one-year-old  child  as  though  he  were  two, 
and  to  him  as  though  he  were  six  ;  for  the 
difference  of  progress  diminishes  in  the  inverse 
proportion  of  years.  Let  the  teacher,  especially 
he  who  is  too  much  in  the  habit  of  attributing  all 
learning  to  teaching,  consider  that  the  child  al- 
ready carries  half  his  world,  that  of  mind, — the 
objects,  for  instance,  of  moral  and  metaphysical 
contemplation, — ready  formed  within  him  ;  and 
hence  that  language,  being  provided  only  with 
physical  images,  cannot  give,  but  merely  illum- 
ine, his  mental  conceptions."  (Richter,  Le- 
vana,  pp.  347-8.) 

99.  In  this  immediate  connection  it  will  be 
profitable  to  give  a  brief  attention  to  the  pop 
ular  expression,  "  Teachers  should  teach  pupils 
how  to  learn,  how  to  use  their  faculties  in  order 
that  they  shall  be  able  to  continue  their  mental 
activities  by  themselves,  in  subsequent  years. ' ' 
It  is  a  plain  fact  in  psychological  phenomena, 
that  nearly  all  the  faculties  of  mind  grow,  ' '  in- 
crease in  size, ' '  by  exercise.  This  is  emphatically 
true  of  the  faculties  of  Thought  and  Attention, 
which  are  energies  of  the  Will.  Education  is  a 
habit.  Hence  no  one  can  be  said  to  know  how 


METHODS   OF  TEACHING.  95 

to  command  his  faculties,  who  has  not  the  habit 
of  it,  called  education.  This  state  is  attained 
by  those,  and  those  only,  who  actually  exert 
their  faculties  to  the  maximum  degrees,  so  that 
this  state  becomes  habitual.  Methods  of  Teach- 
ing regard  these  degrees  as  their  bases  in  Mind. 
Mere  Theory  will  never  produce  these  habits.  All 
teaching  of  pupils  "  how  to  study/ 'which  does 
not  demand  of  them  their  maximum  efforts  in 
practice,  is  a  delusion,  and  a  fatal  deception  to 
the  learners.  The  arm  of  the  smith  does  not 
grow  strong  by  his  standing  at  the  forge  and 
looking  at  the  sledge-hammer,  but  by  wielding 
it.  Intellectual  growth  comes  not  by  thinking 
how  to  study,  but  by  mental  application  in 
studying  up  to  the  measure  of  the  highest  de- 
grees. 

100.  So  far  as  Methods  of  Teaching  are  con- 
cerned,   the   matter    taught  may   be   in   itself, 
either  error  or  truth.     Methods  take  whatever 
subjects,  in  whatever  form  of  text-books  or  ob- 
jects, that  are  set  to  them,  and  convey  them  into 
the  presence  of  the  corresponding  faculties  that 
are  to  learn  these  subjects — this  conveying,  if  ac- 
cording to  a  philosophical  principle,  is  teaching  ; 
for  no  power  external  to  the  mind  of  the  learner 
can  learn  for  that  mind,  nor  compel  it  to  learn. 
The  learning  is  a  matter   within  the  exclusive 
province  of  the  mind  that  is  to  learn,  or  to  be 
taught. 

101.  Methods  of  Teaching  are  not  concerned 
with   what   is    popularly    called    ' '  waking    up 
mind, "  for  if  Methods  assume  any  thing  pre- 


OF 


96  ON   THE   THEORY   OF 

eminently,  it  is  that  subject-matter,  when  set 
before  mind  according  to  the  principles  of  adap- 
tation, will  incite  the  mind  to  activity,  intui- 
tively and  spontaneously.  "  To  wake  up  mind, " 
implies,  in  practice,  the  false  notion  that  the  chil- 
dren are  to  be  excited  or  astonished  at  the  man- 
ner of  the  teacher,  and  at  the  irrelevancy  of  the 
points  he  presents,  rather  than  at  the  value  of 
the  subject-matter  set  before  them  to  be  learn- 
ed. This  is  mere  charlatanism.  Emotional  ex- 
citement, with  dissipation  of  thought,  can  never 
take  the  place  of  calm,  deliberate,  intense  atten- 
tion and  continued  thinking,  when  sound  learn- 
ing is  sought.  Nothing  is  more  pernicious  to 
good  habits  of  thought  than  the  introduction 
into  class-rooms  of  what  is  called  "  variety,"  as 
the  term  is  practically  exemplified.  The  only 
"  variety"  permissible,  is  that  which  follows  upon 
progress,  pointedly,  into  additional  subject-mat- 
ter of  the  lesson,  not  into  this  or  that  subject 
which  has  no  direct  and  close  relationship  to  the 
recitation,  and  which  permits  attention  and  power 
to  be  dissipated,  not  concentrated.  The  mind 
of  childhood  is  always  awake — it  may  need  to 
be  centred  on  this  subject. 

102.  "  Bonnet  calls  attention  the  mother  of 
genius,  but  she  is  in  fact  her  daughter ;  for 
whence  does  she  derive  her  origin,  save  from 
the  marriage  contracted  in  heaven  between  the 
object  and  the  desire  for  it  ?  Hence  attention 
can  really  be  as  little  preached  or  flogged  into 
a  person  as  ability.  ...  A  very  important 
distinction  must  be  drawn  between  the  power  of 


METHODS   OF  TEACHING.  97 

attention  diffused  among  the  generality  of  men, 
and  that  appertaining  solely  to  men  of  genius. 
The  latter  can  only  be  recognized,  protected,  and 
cherished,  but  not  created.  ...  On  the 
other  hand,  common  every-day  attention  needs 
not  so  much  to  be  aroused,  as  to  be  distributed 
and  condensed  ;  even  careless,  inattentive  chil- 
dren possess  the  faculty,  but  it  is  dissipated  upon 
all  passing  objects.  ...  In  what  manner 
can  you  arouse  the  innate  desire  of  mental  prog- 
ress ?  The  impulses  of  the  senses  excite  and 
then  stupefy,  but  help  not  to  produce  it.  To 
overwhelm  the  mind  with  lessons,  that  is,  with 
mere  summaries  of  accounts,  resembles  the  Si- 
berian custom  of  giving  the  sacrament  of  the 
Lord's  Supper  to  infants.  .  .  .  Philosophy 
begins  with  what  is  highest  and  most  difficult ; 
mathematics,  with  what  is  nearest  and  easiest. 
.  What,  then  remains  ?  The  metaphys- 
ics of  the  eye  ;  the  knowledge  forming  the 
boundary  between  experience  and  abstraction. " 
(Richter,  Levana,  pp.  353-9.) 

103.  "  To  Excite  (Latin,  excitare)  is  to  call 
out  into  greater  activity  what  before  existed 
in  a  calm  or  calmer  state,  or  to  rouse  to  an 
active  state  faculties  or  powers  which  before 
were  dormant.  The  term  is  also  used  of  purely 
physical  action.  We  excite  heat  by  friction. 
Awaken  (A.  S.,  awaccian,  awecian)  is  to 
rouse  from  a  state  of  sleep,  or,  analogously,  to 
rouse  any  thing  that  has  lain  quiet,  and,  as  it 
were,  dormant,  as  to  awaken  suspicion,  and  is 
applicable  only  to  intelligent  subjects.  Bouse 


98  ON  THE   THEOKY   OF 

(A.  S.,  rasian)  is  to  awaken  in  a  sudden  or  start- 
ling manner,  so  as  to  bring  into  an  energetic 
state  by  a  strong  impulse.  To  incite  (Latin, 
incitare)  is  to  excite  to  a  specific  act  or  end 
which  the  inciter  has  in  view.  To  stimulate  is 
to  quicken  into  activity  (stimulus,  a  spur) 
and  to  a  certain  end.  Men  are  incited  when 
their  passions  are  roused  ;  they  are  stimulated 
when  they  are  induced  to  make  greater  exer- 
tions, as  by  a  hope  of  reward  or  any  other  exter- 
nal impulse.  They  are  awakened  out  of  indiffer- 
ence, roused  out  of  lethargy  and  torpor,  incited 
by  the  designing  influences  of  others,  stimulated 
by  new  motives  of  action.  Men  are  incited  to 
what  otherwise  they  would  not  have  given  their 
efforts.  They  are  commonly  stimulated  to 
something  which  they  are  pursuing,  or  intend- 
ing to  pursue,  but  with  want  of  energy. " 
(Smith,  Syn.  JDiscr.) 

104.  As  to  the  Form  in  which  knowledge 
is  left  in  the  mind,  when  all  the  circumstances 
attending  the  presentation  have  been  rigidly 
based  upon  the  nature  of  the  case,  Methods  of 
Teaching  have  no  responsibility — that  ends  when 
the  presentation  is  completed.  The  mind,  as  a 
cause  unto  itself,  and  its  prior  state  of  knowl- 
edge, are  responsible  for  the  form  or  impression, 
in  which  the  matter,  under  these  conditions,  ex- 
ists within  itself.  If  this  form  lacks  certitude, 
or  "  material  truth  in  the  absolute  sense,"  it 
can  only  be  corrected  by  presenting  to  the  learn- 
ing mind  other  subject-matter.  But  what  this 
subject-matter  shall  be  is  no  concern  of  Methods 


METHODS   OF   TEACHING.  99 

of  Teaching,  as  has  been  shown  in  a  previous 
section  of  this  investigation.  If  the  subject-mat- 
ter be  not  properly  separated  into  parts,  and 
those  parts  sharply  freed  from  adventitious  mat- 
ter, so  that  it  may  be  brought  boldly  and  une- 
quivocally into  the  conscious  presence  of  the  cor- 
responding faculties — if  there  be  a  want  here, 
it  is  the  fault  of  the  System  of  the  teacher. 
Methods  of  Teaching  demand  only  that  the  prin- 
ciples of  adaptation  be  not  violated.  The 
Methods  assume  the  subjects  placed  in  the  hands 
of  the  teacher.  The  teacher  has  two  important 
things  to  do  :  (1)  To  consider  if  his  System  of 
subject-matter  is  so  constructed  that  it  is  capa- 
ble of  being  presented  to  this  individual  learner  ; 
(2)  To  reflect  upon  the  principles  which  under- 
lie the  actual  procedure  of  teaching.  He  must 
attend  to  System  and  then  to  Method. 

106.  In  connection  with  Methods  of  Teaching 
\  one  often  hears  the  expressions,  "  Develop  the 
idea  in  the  mind  of  the  learner, "  "  Lead  the 
mind  gradually  up  to  the  idea. ' '  To  simple  per- 
ception there  can  be  no  development  work,  for 
perception  is  intuitive,  and  is  ultimate  in  its  au- 
thority, upon  the  presence  in  consciousness  of 
the  object.  Development  exists  within  the  Prov- 
ince of  Thought. 

•  Notions,  or  conceptions,  or  ideas,  are  aggre- 
gations of  simpler  elements,  which  constitute  the 
group  or  Unit  of  notions.  When  the  faculties  of 
the  mind  are  too  feeble  to  comprehend  the  unit 
group,  the  elements  of  the  unit  are  separated 
and  set  before  the  mind  of  the  learner  in  sue- 


100  OK   THE   THEORY   OF 

cession  until  all  are  seen  as  one.  The  process 
(Mode),  called  "  development,"  is  that  by  which 
the  teacher  analyzes  and  presents  the  notion  that 
is  to  be  taught,  and  the  synthetical  process  by 
which  the  learner  apprehends,  and  combines  or 
reconstructs,  the  elements  into  a  notion  that  is 
similar  to  that  possessed  by  the  teacher. 

106.  The  process  by  which  a  student  is  in- 
ducted into  a  prehension  and  a  comprehension 
of  an  aggregation  of  ideas,  which  bear  an  inti- 
mate  and  necessary  relation  to   each    other,   is 
called  Thoroughness.     A  student  who  is  thor- 
oughly taught  surveys  from  the  centre,   a  group 
of  ideas  which  constitute  a  structure  created  by 
Thought. 

107.  "  To  Develop  is  to  open  out  what  was 
contained  in  another  thing,  or  the  thing   itself 
(Fr.  developper).     In  develop  these  two  ideas 

,  are  inherent,  the  gradual  opening  of  the  whole 
containing,  and  the  gradual  exhibition  of  the 
particular  contained.  So  we  might  say,  i  Time 
developed  his  character,'  or  '  circumstances  de- 
veloped the  cruelty  which  was  latent  in  his  char- 
acter. '  Unlike  Unfold,  develop  is  not  used  of 
purely  physical  processes.  We  speak  of  the  de- 
velopment of  plans,  plots,  ideas,  the  mind  ;  and 
also  of  the  development  of  the  body  in  growth  ; 
but  these  are  scientific  terms  involving  other* 
ideas,  as  of  the  vital  functions  in  growth.  We 
should  never  speak  of  the  development  of  a  flag 
or  a  tablecloth.  In  other  words,  it  is  not  used 
of  manual  or  mechanical  unfolding.  On  the 
other  hand,  in  the  sense  of  the  mechanical  pro- 


METHODS   OF    TEACHING.  101 

cess  of  gradually  opening,  unfold  is  used  as  well 
as  in  the  other  ;  but  in  this  latter  develop  ex- 
presses far  more  than  unfold,  and  relates  to  the 
laws  of  expansion  by  which  a  thing  unfolds  in 
definite  sequence  of  expansion,  and  in  conform- 
ity with  principles  which  conserve  the  type  de- 
veloped. Hence  we  speak. of  a  true  and  a  vic- 
ious development.  To  Unravel  (old  German, 
reffen,  to  pluck)  is  purely  a  mechanical  effort  of 
separating  what  is  complicated,  whether  naturally 
or  accidentally,  and  expresses  simple  disentangle- 
ment, not  growth  or  expansion.  As  the  former 
indicate  ordinary  processes  of  nature  or  art,  so 
the  latter  indicates  extraordinary  and  counterac- 
tive processes,  and  commonly  implies  the  abnor- 
mal state  of  that  which  needs  to  be  unravelled. 

"  '  Then  take  him  to  develop  if  you  can, 

And  hew  the  block  off  and  get  out  the  man. ' 

Pope. 

u  '  Several  pieces  of  cloth,  the  largest  we  had 
seen  being  fifty  yards  long,  which  they  un- 
folded and  displayed  so  as  to  make  the  greatest 
show  possible.' — Cook's  Voyages. 

4 '  '  What  ridge's  this  ?  Unfold  yourself,  dear 
Robin. ' — Ben  Jonson. 

* '  '  That  great  chain  of  causes  which,  linking 
one  to  another,  even  to  the  throne  of  God  Him- 
self, can  never  be  unravelled  by  any  industry  of 
ours.' — Burke."  (Smith,  Syn.  Discr.,  ed. 
1878,  Develop.} 

108.  Methods  of  Teaching  must  have  refer- 
ence to  the  ways  according  to  which  the  learner's 


102  ON   THE   THEORY   OF 

faculties  proceed  when  he  is  applying  him- 
self to  study.  Unless  this  be  understood,  the 
faculties  of  the  pupil  will  be  embarrassed  in  their 
normal  activities.  This  will  cause  discourage- 
ment to  both  teacher  and  pupil. 

109.  "  There  exist  nevertheless  certain  gen- 
eral modes  of  treating  any  subject  which  can  be 
clearly  distinguished  by  the  student.  Logic 
oannot  teach  him  exactly  how  and  when  to  use 
each  kind  of  method,  but  it  can  teach  him  the 
natures  and  powers  of  the  methods,  so  that  he 
will  be  more  likely  to  use  them  rightly.  We  must 
distinguish : 

"  1.  The  method  of  discovery, 

"  2.  The  method  of  instruction. 

"  The  method  of  discovery  is  employed  in 
the  acquisition  of  knowledge,  and  really  consists 
in  those  processes  of  inference  and  induction,  by 
which  general  truths  are  ascertained  from  the 
collection  and  examination  of  particular  facts. 
The  second  method  only  applies  when  knowl- 
edge has  already  been  acquired  and  expressed  in 
the  form  of  general  laws,  rules,  principles  or 
truths,  so  that  we  have  only  to  make  ourselves 
acquainted  with  these  and  observe  the  due  mode 
of  applying  them  to  particular  cases,  in  order  to 
possess  a  complete  acquaintance  with  the  subject. 

"  A  student,  for  example,  in  learning  Latin, 
dreek,  French,  German,  or  any  well-known  lan- 
guage, receives  a  complete  Grammar  and  Syntax 
setting  forth  the  whole  of  the  principles,  rules 
and  nature  of  the  language.  He  receives  these 
instructions,  and  takes  them  to  be  true  on  the 


METHODS   OF   TEACHING.  103 

authority  of  the  teacher,  or  the  writer  of  the 
book  ;  and  after  rendering  them  familiar  to  his 
mind  he  has  nothing  to  do  but  to  combine  and 
apply  the  rules  in  reading  or  composing  the  lan- 
guage. He  follows,  in  short,  the  method  of  In- 
struction. But  this  is  an  entirely  different  and 
opposite  process  to  that  which  the  scholar  must 
pursue  who  has  received  some  writings  in  an  un- 
known language,  and  is  endeavoring  to  make  out 
the  alphabet,  words,  grammar,  and  syntax  of  the 
language.  He  possesses  not  the  laws  of  gram- 
mar, but  words  and  sentences  obeying  those 
laws  ;  and  he  has  to  detect  the  laws  if  possible 
by  observing  their  effects  on  the  written  lan- 
guage. He  pursues,  in  short,  the  method  of  dis- 
covery consisting  in  a  tedious  comparison  of  let- 
ters, words,  and  phrases,  such  as  shall  disclose 
the  more  frequent  combinations  and  forms  in 
which  they  occur.  The  process  would  be  a 
strictly  inductive  one,  such  as  I  shall  partially 
exemplify  in  the  Lessons  on  Induction  ;  but  it  is> 
far  more  difficult  than  the  method  of  Instruction, 
and  depends  to  a  great  extent  on  the  happy  use 
of  conjecture  and  hypothesis,  which  demands  a 
certain  skill  and  inventive  ability. 

"  Exactly  the  same  may  be  said  of  the  inves- 
tigation of  natural  things  and  events.  The  prin- 
ciples of  mechanics,  of  the  lever,  inclined  plane, 
and  other  Mechanical  Powers,  or  the  Laws  of 
Motion,  seem  comparatively  simple  and  obvious 
as  explained  to  us  in  books  of  instruction.  But 
the  early  philosophers  did  not  possess  such 
books ;  they  had  only  the  Book  of  Nature,  in 


104  O!S"  THE   THEORY   OF 

which  is  set  forth  not  the  laws,  but  the  results  of 
the  laws,  and  it  was  only  after  the  most  patient 
and  skilful  investigation,  and  after  hundreds  of 
mistakes,  that  those  laws  were  ascertained.  It 
is  very  easy  now  to  understand  the  Copernican 
system  of  Astronomy,  which  represents  the  plan- 
ets as  revolving  round  the  sun  in  orbits  of  vari- 
ous magnitude.  Once  knowing  the  theory  we 
oan  readily  see  why  the  planets  have  such  var- 
ious movements  and  positions,  and  why  they 
sometimes  stand  still  ;  it  is  easy  to  see,  too, 
why  in  addition  to  their  own  proper  rrotions 
they  all  go  round  the  earth  apparently  every  day 
in  consequence  of  the  earth's  diurnal  rotation. 
But  all  these  changes  were  exceedingly  puz- 
zling to  the  ancients,  who  regarded  the  earth  as 
standing  still. 

"  The  method  of  discovery  thus  begins  with 
facts  apparent  to  the  senses,  and  has  the  difficult 
task  of  detecting  those  universal  laws  or  general 
principles  which  can  only  be  comprehended  by 
intellect.  It  has  been  aptly  said  that  the  method 
of  discovery  thus  proceeds  from  things  better 
known  to  us,  or  our  senses  (nobis  notiora),  to 
those  whicli  are  more  simple  or  better  known  in 
nature  (notiora  naturae).  The  method  of  In- 
struction proceeds  in  the  opposite  direction,  be- 
ginning with  the  things  notiora  naturae,  and 
proceeding  to  show  or  explain  the  things  nobis 
notiora.  The  difference  is  almost  like  that  be- 
tween hiding  and  seeking.  He  who  has  hidden 
a  thing  knows  where  to  find  it ;  but  this  is  not 
the  position  of  a  discoverer,  who  has  no  clue  ex- 


METHODS   OF   TEACHING.  105 

cept  sucli  as  he  may  meet  in  his  own  diligent 
and  sagacious  search. 

' '  Closely  corresponding  to  the  distinction  be- 
tween the  methods  of  Discovery  and  Instruction 
is  that  between  the  methods  of  Analysis  and 
Synthesis.  It  is  very  important  indeed  that  the 
reader  should  clearly  apprehend  the  meanings  of 
these  terms  in  their  several  applications.  Analy- 
sis is  the  process  of  separating  a  whole  into  its 
parts,  and  synthesis  the  combination  of  parts 
into  a  whole.  The  analytical  chemist,  who 
receives  a  piece  of  mineral  for  examination, 
may  be  able  to  separate  completely  the  several 
chemical  elements  of  which  it  is  composed  and 
ascertain  their  nature  and  comparative  quantities  ; 
this  is  chemical  analysis.  In  other  cases  the 
chemist  mixes  together  carefully  weighed  quan- 
tities of  certain  simple  substances  and  combines 
them  into  a  new  compound  substance  ;  this  is 
chemical  synthesis.  Logical  analysis  and  syn- 
thesis must  not  be  confused  with  the  physical 
actions,  but  they  are  nevertheless  actions  of 
mind  of  an  analogous  character. 

"  In  logical  synthesis  we  begin  with  the 
simplest  possible  notions  or  ideas,  and  combine 
them  together.  We  have  the  best  possible  ex- 
ample "in  the  elements  of  Geometry.  In  Euclid 
we  begin  with  certain  simple  notions  of  points, 
straight  lines,  angles,  right  angles,  circles,  &c. 
Putting  together  three  straight  lines  we  make  a 
triangle  ;  joining  to  this  the  notion  of  a  right 
angle,  we  form  the  notion  of  a  right-angled  tri- 
angle. Joining  four  other  equal  lines  at  right 


106  OST   THE   THEORY   OF 

angles  to  each  other  we  gain  the  idea  of  a 
square,  and  if  we  then  conceive  such  a  square 
to  be  formed  upon  each  of  the  sides  of  a  right- 
angled  triangle,  and  reason  from  the  necessary 
qualities  of  these  figures,  we  discover  that  the 
two  squares  upon  the  sides  containing  the  right 
angle  must  together  be  exactly  equal  to  the 
square  upon  the  third  side,  as  shewn  in  the 
47th  Proposition  of  Euclid's  first  book.  This  is 
a  perfect  instance  of  combining  simple  ideas  into 
more  complex  ones. 

11  We  have  often,  however,  in  Geometry  to 
pursue  the  opposite  course  of  Analysis.  A 
complicated  geometrical  figure  may  be  given  to 
us,  and  we  may  have,  in  order  to  prove  the  prop- 
erties which  it  possesses,  to  resolve  it  into  its 
separate  parts,  and  to  consider  the  properties  of 
those  parts  each  distinct  from  the  others. 

'  i  A  similar  distinction  between  the  analytical 
and  synthetic  methods  can  be  traced  throughout 
the  natural  sciences.  By  keeping  exact  registers 
of  the  appearance  and  changes  of  the  weather 
we  may  readily  acquire  an  immense  collection  of 
facts,  each  such  recorded  fact  implying  a  multi- 
tude of  different  circumstances  occurring  to- 
gether. Thus  in  any  storm  or  shower  of  rain 
we  have  to  consider  the  direction  and  force  of 
the  wind  ;  the  temperature  and  moistness  of  the 
air  ;  the  height  and  forms  of  the  clouds  ;  the 
quantity  of  rain  which  falls,  or  the  lightning 
and  thunder  which  occur  with  it.  If  we  pro- 
ceed by  analysis  only  to  explain  the  changes  of 
the  weather  we  should  have  to  try  resolving 


METHODS   OF   TEACHING.  107 

each  storm  or  change  of  weather  into  its  separate 
circumstances,  and  comparing  each  with  every 
other  to  discover  what  circumstances  usually  go 
together.  We  might  thus  ascertain  no  doubt 
with  considerable  certainty  what  kinds  of  clouds, 
and  what  changes  of  the  wind,  temperature, 
moisture,  <fec.,  usually  precede  any  kind  of 
storm,  and  we  might  even  in  time  give  some  im- 
perfect explanation  of  what  takes  place  in  the 
atmosphere. 

"  But  we  might  also  apply  with  advantage 
the  synthetical  method.  By  previous  chemical 
investigations  we  know  that  the  atmosphere 
consists  mainly  of  the  two  fixed  gases,  oxygen 
and  nitrogen,  with  the  vapour  of  water,  the  latter 
being  very  variable  in  quantity.  We  can  try 
experimentally  what  takes  place  when  portions 
of  such  air  of  various  degrees  of  moistness  are 
compressed  or  allowed  to  expand,  or  are  mixed 
together,  as  often  happens  in  the  atmosphere. 
It  is  thus  discovered  that  whenever  moist  air  is 
allowed  to  expand  cloud  is  produced,  and  it  may 
be  drops  of  rain.  Dr.  Hutton,  too,  found  that 
whenever  cold  moist  air  is  mixed  with  warm 
moist  air  cloud  is  again  produced.  We  can 
safely  argue  from  such  small  experiments  to 
what  takes  place  in  the  atmosphere.  Putting 
together  synthetically,  from  the  sciences  of 
chemistry,  mechanics,  and  electricity,  all  that 
we  know  of  air,  wind,  cloud  and  lightning,  we 
are  able  to  explain  what  takes  place  in  a  thunder- 
storm far  more  completely  than  we  could  do  by 
merely  observing  directly  what  happens  in  the 


108  ON  THE  THEORY   OF 

storm.  We  are  here  however  anticipating  the 
methods  of  inductive  investigation,  which  we 
must  consider  in  the  following  lessons.  It  wiM 
appear  that  Induction  is  equivalent  to  analysis, 
and  that  the  deductive  kinds  of  reasoning  which 
we  have  treated  in  prior  lessons  are  of  a  synthetic 
character. 

11  It  has  been  said  that  the  synthetic  method 
usually  corresponds  to  the  method  of  instruction 
and  the  analytic  method  to  that  of  discovery. 
But  it  may  be  possible  to  discover  new  truths  by 
synthesis  and  to  teach  old  ones  by  analysis.  Sir 
John  Herschel  in  his  well-known  Outlines  of 
Astronomy  partially  adopts  the  analytic  method  ; 
he  supposes  a  spectator  in  the  first  place  to  survey 
the  appearances  of  the  heavenly  bodies  and  the 
surface  of  the  earth,  and  to  seek  an  explanation  ; 
he  then  leads  him  through  a  course  of  arguments 
to  show  that  these  appearances  really  indicate 
the  rotundity  of  the  earth,  its  revolution  about 
its  own  axis  and  round  the  sun,  and  its  subor- 
dinate position  as  one  of  the  smaller  planets  of 
the  solar  system.  Mr.  Norman  Lockyer's  Ele- 
mentary Lessons  in  Astronomy  is  a  clear  example 
of  the  synthetic  method  of  instruction  ;  for  he 
commences  by  describing  the  sun,  the  centre  of 
the  system,  and  successively  adds  the  planets 
and  other  members  of  the  system,  until  at  last 
we  have  the  complete  picture  ;  and  the  reader 
who  has  temporarily  received  everything  on  the 
writer's  authority,  sees  that  the  description  cor- 
responds with  the  truth.  Each  method,  it  must 


METHODS   OF  TEACHING.  109 

be  allowed,   has  its  own  advantages.     (Jevons, 
Lessons  in  Logic,  ed.  1878,  pp.  202-208.) 

110.  Methods  of  Teaching  must  respect  that 
inherited  and  national  l '  cast  of  mind  ' '  which 
exhibits  itself  so  prominently  that  it  forms  an 
important  element  in  teaching.  Those  national 
bents  of  mind,  traits  of  disposition,  and  survival 
of  tendencies,  constitute  a  "  prior  knowledge," 
or  setting,  which  gives  form  to  the  knowledge 
presented  by  the  teacher.  The  Italian  mind  in- 
herits peculiar  adaptations  for  music.  The  Ger- 
man mind,  as  revealed  in  the  language,  is  dis- 
posed to  aggregate  and  accumulate  conceptions. 
The  native  tendency  with  the  French  mind,  in 
language,  is  towards  separation  and  analysis. 
The  English  mind,  in  language,  evidently  has 
its  form  in  directness,  neither  cumulative  nor 
over  analytical.  With  some  nations,  gesticulation 
forms  a  prominent  inheritance  of  the  people. 
The  United  States,  being  peopled  from  all  na- 
tions, present  a  multitude  of  national  peculiari- 
ties to  the  teacher,  who,  herein,  has  a  more  deli- 
cate work  before  him  than  teachers  who  labor 
with  a  single  nationality.  This  element,  although 
subtle,  is  powerful  in  any  place  where  the  schools 
are  composed  of  children  of  many  nationalities. 
While  the  psychological  faculties  are  the  same 
in  kind  and  function  among  all  peoples,  yet  the 
native  quality  of  these  faculties,  or  the  bent 
for  giving  form  to  knowledge,  varies  with  the 
peoples.  These  native  qualities  or  bents  are  not 
the  differences  in  degrees  of  the  same  capacities 
of  people  of  the  same  nationality.  They  are 


110  ON   THE   THEORY   OF 

powers  or  forces  wliich  necessarily  modify  the 
form  of  the  same  matter  which  is  set  before  all 
alike.  This  is  done  unconsciously  to  the  chil- 
dren who  are  taught. 

111.  Methods   of  Teaching   are  difficult   to 
suit,  "  as  an  object  to  a  quality,"  in  their  daily 
application,  by  reason  of  the  intricacy  and  eva- 
nescence of  psychological  phenomena.     But  the 
province  is  established.      The  very  delicacy  and 
mutability  of  the  modifications  of  Mind  lend  a 
zest  to  Methods,  and  consequently  to  teaching, 
that  must    emphatically  and  forever  banish   all 
tendencies  to  mere  routine  and  formalism,  when 
teachers  fully  grasp  the  Spirit  of  Methods.     Gen- 
uine Methods  of  Teaching,  from  their    nature, 
must  be  universally  successful  for  accomplishing 
their   objects.     A    principle  can   never  become 
spiritless — the  application  of  it  may,  if  it  be  an 
unintelligent  one,  but  the  principle  must  be  as 
constant  and  as  enduring  as  the  subjects  to  which 
it  relates,  or  out  of  which  it  springs. 

112.  Methods  of  Teaching    are    not,  in  the 
present  state  of  psychological  science,  absolutely 
invariable.     The  one  element  in  the  foundations, 
that  of  subject-matter,  is  firm,  as  science  is  firm. 
The  other  element  in  the  foundations,  that  of 
psychology,  is  less  firm,  perhaps,  because  the  Sci- 
ence of  Mind  is  not  so  well  established  in  its  full- 
ness as  are  most  other  sciences  which  are  pursued 
in  schools.     No  science  or  art  is  more  stable  or 
lasting  than  its  foundations.     However,  the  main 
principles  of  the  science  of  psychology  are  very 
thoroughly    established,  as   they   appear   to-day 


METHODS   OF  TEACHING.  Ill 

rising  up  out  of  hundreds  of  years  of  diligent 
study  by  the  philosophers  of  the  past  and  the 
present.  "  In  mental  philosophy  the  general 
statements  have  commonly  a  genuine  fact,  hut 
mixed  with  this  there  is  often  an  alloy.  The 
error  may  not  influence  the  spontaneous  action 
of  the  primitive  principle,  but  it  may  tell  disas- 
trously or  ludicrously  in  the  reflex  application. ' ' 
(McCosh,  Int.  of  Mind,  p.  60,  ed.  1870.) 

113.  What  are  ordinarily  denominated  ' '  class- 
drill  "  and  "  examinations, "   are  no  legitimate 
elements  in  the  conception  of  Methods  of  Teach- 
ing.    They  are  no  new  things — they  are  mere 
repetitions.     The  value  of  repetition  is  purely  a 
psychological  problem,  not  belonging  to  subject- 
matter  and  mind,  as  do  the  problems  of  Methods. 
"  Repetition,  else  the  mainspring  of  instruction, 
is  the  chief  destroyer  of  attention  ;  because,  in 
order  to  give  attention  to  what  is  repeated,  you 
must  first  have  found  it  worthy  of  a  still  greater 
exertion  of  that  faculty."     (Richter,  Levana,  p. 
356.) 

1 14.  Methods  of  Teaching,  from  their  nature, 
forbid  the  so-called  Individuality  of  any  teacher 
to  enter  into  them,  as  a  constituent  part  of  their 
essence.     The  foundations  of  the  Methods  being, 
the  principles  of    adaptation    between  subject- 
matter  and  mind,  the  eccentricities,   idiosyncra- 
sies, or  peculiarities  of  any  one  mind  form  no  fac- 
tor in  the  Science  and  Art  of  Methods  of  Teach- 
ing.     "  Every  mind  is  more  or  less  like  every 
other  mind  ;  there  is  always  a  basis  of  similarity, 
but    there  is  a  superstructure   of  feelings,    im- 


112  ON   THE   THEORY   OF 

pulses,  and  motives  which  is  distinctive  for  each 
person.77  (Jevons,  Princ.  of  Science,  p.  733, 
ed.  1877.) 

1 15.  Teachers  have  their  individuality,  which 
shows  itself  in  greater  or  less  degrees  in  their 
school-room  practice,  while  applying  philosophi- 
cal Methods  of  Teaching.  This  individuality  is 
exhibited  in  the  way  that  one  teacher  illustrates  a 
point  differently  from  another — in  the  way  he 
speaks — in  the  way  he  looks — in  the  way  he 
thinks,  it  may  be — in  the  way  in  which  his 
questions  are  conceived — in  the  impromptu  ex- 
pedients which  he  devises — in  what,  in  general, 
is  called  "  his  way  of  doing  things."  This  in- 
dividuality of  the  teacher  is  known  as  Manner. 
Misapprehension  of  the  true  province  of  scientific 
Methods  of  Teaching  has  led  many  to  apply  the 
term  to  any  peculiar  experiment  or  expedient 
which  may  be  selected,  which  things  are  in  fact 
but  examples  of  Manner.  The  familiar  expres- 
sions so  often  heard — ' l  my  method  is  thus  and 
so, "  "  my  method  is  not  that,  but  this, ' '  "  I 
illustrate  by  this  method,  using  a  bundle  of 
sticks  instead  of  kernels  of  corn'7 — are  simply  ex- 
amples of  Manner. 

-  116.  A  teacher  has  his  own  Manner  of 
Teaching — he  can  not  have  his  Method,  be- 
cause Methods  are  general  or  universal  principles, 
which  are  beyond  the  exclusiveness  of  the  indi- 
vidual. Mannerisms  can  be  affected  or  imitated, 
or  devised,  or  invented  ;  but  Methods  of  Teach- 
ing, existing  originally  in  the  native  constitution 
of  things,  can  not  be  invented — they  must  be 


METHODS   OF   TEACHING.  113 

discovered.  Being  discovered,  they  are  no 
more  his  who  discovers  them,  than  the  principle 
of  gravity  is  the  property  of  Newton  because  he 
discovered  its  nature  and  laws. 

117.  This  conception  of  Methods  of  Teaching 
should  not  be  confused  with  that  of  Methods  in 
general,  which  are  ways  of  procedure  in  the  in- 
vestigations of  subject-matter  only — they  do  not 
aim  at  mind.     Such  expressions  as  "  Homer's 
Method  of  Approximation, "  and  the  like,  cor- 
rectly use  the  word  Method. 

118.  In  the  subjoined  quotation  the  terms 
Manner  and  Method  are  not  sufficiently  discrimi- 
nated in  demarcation — each  includes  portions  of 
the  conception  of  Mode. 

'  *  Perhaps  this  difference  between  method  and 
manner  will  appear  better  if  we  use  an  illustration 
which  is  supported  by  the  etymology  of  the 
word  method  :  Suppose  it  is  proposed  to  estab- 
lish a  connection  between  two  cities,  for  this 
purpose  a  road  is  made  ;  this  road  will  be  used 
by  all  that  go  from  one  city  to  the  other,  and  by 
all  kinds  of  individuals  ;  it  is  the  same  road 
for  all  and  not  liable  to  be  changed  by  individual 
whims  or  notions.  But  the  manner  in  which 
the  road  is  used  varies  very  much  ;  some  will 
walk,  others  will  run,  and  others  still  will  ride. 
The  road  in  our  illustration  represents  the 
method  in  pedagogics  ;  it  may  be  used  by  the 
most  widely  different  individualities  ;  the  way 
in  which  people  make  use  of  it  is  the  manner. 
Manner  cannot  be  thoroughly  specified  or  de- 
fined. Here  the  utmost  freedom  must  be  allowed 


114  OX   THE   THEORY    OF 

to  teachers  and  pupils  to  develop  their  own  in- 
dividualities. "  (Soldan,  art.  Method  and  Man- 
ner, Nat.  Ed.  Ass.  Proceedings,  1874,  p.  249.) 

119.  When  the  Manner   of   a   teacher   has 
"  method  in  it," — when  it  is  more  or  less  deter- 
mined into  a  System — when  it  has  become  a 
somewhat  systematized  exposition  or  application 
of  the  principle  of  adaptation,  i.e.,  of  Methods 
of  Teaching, — when  Manner  has    assumed  this 
state,  it  is  called  Mode. 

120.  Methods  of  Teaching  are  fundamental 
and   general   principles    "  out   of   which    other 
matters  of   a  speculative  or  practical  character 
flow,  and   become  its  practical  illustrations" — 
they  must  be  discovered,  if  known.     They  can 
be  investigated  in  their  nature — they  can  not  be 
copied,  imitated,  or  assumed — they  can  only  be 
stated  as  principles,  which  can  be  illustrated  or 
exemplified  in  practice  in  certain  ways  called 
Modes,  and  sometimes  Manners.     Manner  is  the 
term  which  contains  prominently  the  individual- 
ity of  the  teacher.     Mode  refers  to  the  systematic 
application  or  illustration  of  Methods — it  has  lit- 
tle of  the  notion  of  individuality  in  it.     Manner- 
can   be   imitated,    but    hardly   taught.       Mode 
can  be  imitated  and  taught.     If  a  teacher  writes 
out  a  lesson  in  a  methodical  order,  point  by  point, 
and  question  by  question,  such  lesson  is  his  Mode 
— and  it  may  partake  of  his  Manner.     The  more 
nearly  teachers  comprehend  the  nature  of  sub- 
ject-matter as  related  to  knowing  mind,  and  the 
mind  itself,  the  more  nearly  will  their  Modes  be 
identical  when  teaching  the  same  subject-matter 


METHODS    OF   TEACHING.  115 

to  classes  of  similar  attainments — and  the  less  of 
mannerisms  will  be  exhibited  by  the  teachers. 

121.  If   perfection    of    knowledge    and    of 
adaptation  were  possible,  it  is  extremely  prob- 
able that  all  perfect  teaching  would  set  the 
same  subjects  to  the  same  pupils  in  exactly  the 
same  Mode,  which  would  then  reach  a  perfect 
illustration  of  Method  of  Teaching. 

122.  The  failure  to  discriminate  the  prov- 
inces  of    Methods   of    Teaching,    Modes,    and 
Manners,  has  led  to  considerable  abuse  of  the 
former  expression.     Mode  and  Manner  can  be 
imitated  by  those  even  who  do  not  comprehend . 
the  principle  which  is  illustrated  ;  supposing  a 
principle  involved  in  the  case,  which  principle  is 
sometimes  wholly  imaginary  in  actual  practice. 
This  being  the  state  of  affairs,  teachers  who  rest 
satisfied  with  copying  another's  Mode  or  Manner 
must  fail,  because  they  do  not  apprehend  the 
animating  principle,   the  Method  of   Teaching, 
which    underlies    the    Mode    imitated.     Those 
teachers  are  dealing  with  the  mere  dress,  lifeless 
forms,  of  Methods.     Methods  are  life,  enduring 
as  mind.     Modes  have  a  portion  of  the  life  of 
Methods,  and  a  portion  from  that  of  the  teacher. 
Manner  has  only  the  life  of  the  teacher  whose 
it  is. 

123.  "  While  Mode  (Lat.  modus)  is  also  ap- 
plicable to  way  of  being,  Manner  (Fr.  maniere) 
denotes  way  of  action.     Manner,  too,  is  casual  ; 
mode,  systematic.     Mode  might  be  defined  reg- 
ular  manner.       Hence  manner   of    action    im- 
plies voluntariness  on  the  part  of  the  agent  ; 


116  OK    THE   THEOKY    OF 

mode  of  action,  uniformity  in  the  thing  acting. 
Modes  of  existence.  Manners  of  conduct  or  oper- 
ation." (Smith,  Syn.  Discr.,  Mode.)  "  In 
consequence  of  the  authorship — there  being  a 
large  number  of  different  writers — there  is  great 
variety  in  the  modes  of  treatment."  (The 
Nation,  No.  700,  p.  340,  Nov.  28,  1878.) 
"  We  all  remember  how  rapidly  the  theory 
grew  up  that  in  the  greenbacks  we  had  stumbled, 
by  a  happy  accident,  on  a  new  mode  of  acquir- 
ing wealth  and  avoiding  financial  convulsions, 
and  how  rapidly,  too,  in  many  minds,  they  began 
to  wear  the  air  of  weapons  of  war,  like  a  grand- 
father's sword  or  musket,  hallowed  by  associa- 
tions, and  unfit  subjects  for  scientific  examination 
or  treatment."  (Ibid.,  No.  704,  p.  394,  Dec. 
26,  1878.)  "  Washburn's  Outlines  of  Criminal 
Law,  A  Manual  of  Criminal  Law,  including  the 
Mode  of  Procedure  by  which  it  is  enforced. ' ' 
(Ibid.,  No.  704,  Dec.  26,  1878.) 

124.  "  System  (Gr.  avarrj^a,  from  awi- 
Gravai,  to  place  together)  regards  fixed  sub- 
jects which  have  rational  dependence  or  con- 
nection. Method  (Gr.  JUST  a,  after,  and  odos, 
a  way)  regards  fixed  processes.  System  is  logi- 
cal or  scientific  collocation.  Method  is  logical 
or  scientific  procedure.  But,  inasmuch  as  a 
mode  of  procedure  may  be  itself  harmonized, 
system  is  frequently  used  in  place  of  method. 
"We  sometimes  say,  '  to  go  systematically  to 
work,'  meaning  methodically.  Method  lays 
down  rules  for  scientific  inquiry,  and  is  the  way 
which  leads  to  system.  '  All  method,'  says  Sir 


METHODS   OF  TEACHING.  117 

W.  Hamilton,  '  is  a  rational  progress — a  prog- 
ress toward  an  end.'  When  Watts  says,  '  The 
best  way  to  learn  any  science  is  to  begin  with  a 
regular  system,  or  a  short  and  plain  scheme  of  that 
science  well  drawn  up  into  a  narrow  compass,  * 
he  is  recommending  a  method."  (Smith,  Syn. 
Discr.,  art.  System.}  "  System  is  a  connected 
body  of  knowledge. ' '  (Jevons,  El.  Les.  Logicy 
p.  346.) 

125.  In  the  following  quotation,  the  defini- 
tions are  not  strictly  accurate,  although  they  ex- 
press the  outlines  : — ' i  In  pedagogy,  method  is 
the  way  chosen,  the  order  followed  by  the  teacher 
to  put  his  own  thought,  his  intelligence,  in  re- 
lation with  the  intelligence  of  his  pupils  ;  mode 
is  the  way  of  organizing  the  school  according  as 
it  is  desired  to  convey  lessons  directly  or  indi- 
rectly to  the  pupils  ;    and  procedures  are  the 
secondary  means,   ordinarily  mechanical,   which 
are  used  to  assure  the  success  of  the  method. 
They  depend  generally  on  the  mode  adopted. ' ' 
(L.  Mariotti,  Conferences  de  Pedagogie,   p.  146, 
ed.  1873,  Paris.) 

126.  In    the    following    quotation    (£),    or 
"  Applied/'  under  both  the  general  and  the 
special,  contains  the  conception  of  Mode. 

"Definition  of  Method. 

"General:  (a)  Theoretical: — The  laws  ac- 
cording to  which  the  ten- 
dency to  acquire  knowledge, 
exerts  itself,  arranged  so  as- 


118  ON  THE  THEORY   OF 

to  show  their  natural  order 
and  relations. 

(b)  Applied:  —  The  same  laws 
translated  into  rules,  and  ar- 
ranged in  the  same  order. 
'"  Special:  (a)  Theoretical: — The  laws  ac- 
cording to  which  the  ten- 
dency to  acquire  a  knowl- 
edge of  Physics,  Logic,  &c., 
•exerts  itself,  arranged  so  as 
to  show  uieir  natural  order 
and  relations. 

(6)  Applied: — -The  same  laws 
translated  into  rules,  and  ar- 
ranged in  the  same  order. ' ' 
(The  late  J.  W.  Arm- 
strong, D.D. — A  Paper  on 
Method.) 

127.  "  The  tendency  of  any  power  or  force 
to  act  in  any  particular  way  is  called  a  Principle, 
The  particular  way  in  which  a  tendency  operates 
is  called  a  Law.     The  statement  of  a  law  in  such 
form  as  will  adapt  it  to  the  solution  of  problems 
is  called  a  Rule."     (Ibid.) 

128.  (a)    Method,    Mode,   and  Manner  of 
Teaching,  may  be  illustrated  and  contrasted,  per- 
haps not  inaptly,  by  the  following  supposition  : 
Suppose  an  engineer  desires  to  span  a  stream  by 
a  bridge — (1)  he  rears  his  abutments  on  either 
side — (2)  he  places  the  main  timbers  or  "  string- 
ers' '  from  abutment  to  abutment  across  the  chasm 
— (3)   he  lays  a  roadway  of  planks  upon  the 
stringers — (4)  he  travels  across  the  gulf  upon 


METHODS   OF  TEACHING. 

the  bridge.  In  the  analogy,  (1)  rearing  the  abut- 
ments corresponds  to  the  acquisition  of  a  knowl- 
edge of  subject-matter  (say  arithmetic),  and  of 
mind  of  the  learner  (Psychology),  by  the  teacher 
— (2)  throwing  the  stringers  across  the  stream 
illustrates  the  process  of  discovering  the  principles 
of  adjusting  subject-matter  to  the  mind  of  the 
learner,  which  is  the  Method  of  Teaching — (3) 
covering  these  stringers  (which  represent  the 
principles  of  connection)  with  a  flooring  of  what- 
ever nature,  suggests  the  invention  of  a  Mode  of 
Teaching — (4)  the  general  or  the  particular 
"air,"  or  "style/'  or  "  bearing,'7  of  the 
teacher  while  teaching  (crossing  the  bridge)  indi- 
cates his  Manner  of  Teaching.  Manner  also  in- 
cludes a  little  of  the  notion  of  the  flooring,  as 
that  a  part  of  it  is  laid  of  wood,  a  part  of  iron, 
according  to  the  fancy  of  the  engineer. 

(b)  Another  illustration  : — "  Another  thing — 
at  Hillard  on  the  Pacific  railway — on  the  use  of 
which  Eastern  people  venture  queer  conjectures, 
is  a  high,  narrow  tressel-work  bridge  supporting 
a  V-shaped  trough — an  object  familiar  enough  to 
residents  of  the  Pacific  Coast.  This  is  a  l  flume, ' 
and  the  wood  used  in  the  kilns  is  floated  through 
it  for  a  distance  of  twenty -four  miles  from  the 
mountains.  Over  2,000,000  feet  of  lumber 
were  necessary  in  its  construction,  and  from 
its  mouth  it  falls  2,000  feet,  the  stream  rush- 
ing through  it  and  sweeping  the  logs  on  its 
bosom  with  a  rapidity  and  ease  that  makes  us 
wonder  why  people  ever  haul  wood  in  cumber- 
some waggons."  (D.  Appleton  &  Co.,  The  Art 
Journal,  New  Series,  No.  27,  p.  71.) 


120  ON  THE   THEORY   OF 

In  this  illustration,  the  principle  of  conveyance 
is  known  in  popular  language  as  the  "  buoying 
up  power  of  water, ' '  the  relative  specific  gravity. 
This  is  the  Method, — by  floating  on  water.  The 
contrivance,  a  V-shaped  trough,  instead  of  the 
surface  of  a  river,  exhibits  the  Mode  of  applying 
the  principle  or  Method.  Whatever  is  peculiar, 
or  individual  about  the  trough,  or  the  prepara- 
tion of  the  wood,  or  the  letting  of  the  water  into 
the  flume,  indicates  the  Manner  involved  in  the 
•case. 

(c)  Another  illustration  : — "  A  railroad  has 
been  constructed  to  the  mines  of  Summit  Hill, 
about  nine  miles  W.  of  the  town  (Mauch  Chunk 
— Mawk  Chunk' — in  Pennsylvania).  The  cars, 
loaded  with  coal,  descend  by  their  own  gravity 
to  the  landing,  and  after  being  emptied  have 
been  heretofore  drawn  up  the  plane  by  mules. 
But  now  the  labors  of  the  mules  are  superseded. 
A  '  back  track  '  has  been  constructed,  which  is 
regarded  as  a  master  piece  of  bold  and  success- 
ful engineering.  From  the  chutes  where  the 
coal  cars  are  unloaded  at  the  town  of  Mauch 
Chunk,  they  return  by  their  own  weight  to  the 
foot  of  Mount  Pisgah.  They  are  then  drawn 
to  the  top  of  that  mountain  on  an  inclined  plane 
by  means  of  a  stationary  engine.  From  the 
liead  of  this  plane  they  pass  by  their  own  gravity 
along  a  railway  of  6  miles,  to  the  foot  of 
another  inclined  plane.  To  the  top  of  this  they 
are  again  raised  by  steam,  and  thence  descend  to 
the  different  mines,  where  they  are  filled  with 
coal,  and  again  descend  by  their  own  weight  to 


METHODS   OF  TEACHING.  121 

the  chutes."  (J.  Thomas,  Lippincottfs  Pro- 
nouncing Gazetteer ,  ed.  1868,  Mauch  Chunk.) 

In  this  illustration,  three  principles  of  motive 
power  are  introduced — gravity,  animal-power, 
and  steam.  They  are  the  Methods  of  transpor- 
tation. The  principle  of  gravity  is  utilized  by 
carriages  on  wheels,  instead  of  carriages  on  run- 
ners ;  the  principle  of  animal -power  was  utilized 
by  using  mules,  instead  of  horses  ;  the  principle 
of  steam-power  is  utilized  by  means  of  a  sta- 
tionary, instead  of  a  movable,  engine.  The  car- 
riages on  wheels,  the  mules,  and  the  stationary 
engine,  arc  objects  which  are  used  to  apply  the 
Methods,  and  are  Modes  of  transportation. 
Whatever  is  individual,  or  peculiar,  in  any  of 
these — not  necessary,  used  instead  of  something 
else  in  form,  rate  of  motion,  or  way  of  applica- 
tion, or  in  construction, — exhibits  Manner. 

(d)  Another  illustration  : — A  gentleman  em- 
ploys a  span  of  horses  to  draw  his  carriage. 
Horse-power  is  the  principle  involved  in  convey- 
ing— it  is  the  Method  of  transporting  the  car- 
riage. A  carriage  on  wheels  is  used,  instead  of 
a  sleigh,  or  ' '  carriage  on  runners, ' '  as  the  way 
of  showing  the  application  of  the  principle  of 
horse-power — this  represents  the  Mode  of  con- 
veyance used  by  the  gentleman.  His  particular 
kind  of  carriage  is  a  landau,  instead  of  a  wag- 
onette— this  notion,  together  with  whatever  of 
' '  style, ' '  or  "  air, ' '  he  may  choose  to  introduce, 
exhibits  his  Manner  of  riding  in  his  landau. 
(See,  also,  Mill's  use  of  these  terms  in  §  224.) 

129.  Mr.  Page  uses  Mode  correctly  in  this  : 


122  ON  THE   THEORY   OF 

"  Right  Modes  of  Teaching^  -Pouring-in  Pro- 
cess, or  lecturing  ;  Drawing-  out  Process,  or 
questioning."  (Theory  and  Practice  of  Teach- 
ing, p.  5,  Contents,  ed.  1853.) 

130.  The  subjoined  illustrates  Mode,   Man- 
ner, and  the  idea  of  * '  leading' '  the  pupil  : 

i 'The  class  were  puzzled  to  understand  the 
resistance  of  the  various  media.  '  I  do  not 
know  as  I  understand  what  media  means/  said 
one  of  the  boys.  '  A  medium  is  that  in  which 
a  body  moves, '  read  the  teacher  from  a  book. 
4  A  medium  ?  '  '  Yes  ;  we  say  medium  when 
we  mean  but  one,  and  media  when  we  mean 
more  than  one.'  After  a  time,  the  pupil  still 
gaining  no  light,  the  regular  teacher  approached  : 
'  John, ' — taking  his  watch  in  his  hand — 
'  would  this  watch  continue  to  go,  if  I  should 
drop  it  into  a  pail  of  water  ? '  i  I  should  think 
it  would  not  long. '  '  Why  not  ? '  '  Because 
the  water  would  get  round  the  wheels  and 
stop  it,  I  should  think. '  l  How  would  it  be  if  I 
should  drop  it  into  a  quart  of  molasses  ? '  The 
boys  smiled.  i  Or  into  a  barrel  of  tar  ? '  *  Sup- 
pose I  should  force  it,  while  open,  into  a  quantity 
of  lard. '  John  said,  '  The  watch  would  not  go 
in  any  of  the  articles.'  '  Articles,  why  not 
say  Media?'  *  Oh,  I  understand  it  now.'  " 
(Ibid.,  pp.  319-321.) 

131.  In  the  annexed  extract,  the  author  uses 
"  Manner"  properly,  but  substitutes  Method  for 
Mode  :  "  The   agreeable    talents  are   too  much 
confined  to  method.     They  are  rendered  too  ab- 
stracted by  being  reduced  to  maxims  and  pre- 


METHODS   OF  TEACHING.  123 

cepts  ;  and  hence  those  things  which  should 
constitute  the  amusement  of  young  people,  are 
made  disgusting  to  them,  as  the  study  of  an  art. 
I  cannot  conceive  any  thing  more  ridiculous,  than 
to  see  an  old  singing  or  dancing-master,  approach 
a  young,  lively,  giggling  girl,  with  a  frigid  and 
formal  air  ;  and  assume,  in  teaching  his  frivolous 
science,  a  more  pedantick  and  magisterial  tone, 
than  if  he  were  teaching  her  the  catechism.  Is 
it  that  the  art  of  singing,  for  instance,  depends 
on  the  knowledge  of  written  musick  ?  Is  it  not 
possible  to  acquire  a  just  command  of  voice,  to 
learn  to  sing  with  taste,  and  even  to  accompany 
an  instrument,  without  knowing  a  single  note  ? 
Is  the  same  manner  of  singing  adapted  to  all 
voices  ?  Doth  the  same  method  of  teaching 
suit  equally  every  genius  ?  It  is  impossible  to 
make  me  believe,  that  the  same  attitudes,  the 
same  steps,  the  same  motions  and  gestures,  or 
even  the  same  dances,  are  equally  proper  for  a 
little,  lively,  sharp-eyed  brunette,  and  a  tall 
beauty  with  languishing  eyes  and  flaxen  hair. 
When  I  see  a  dancing-master  give  the  same  les- 
son, therefore,  indiscriminately  to  both,  I  say 
to  myself,  this  man  follows  the  customs  of  hi& 
profession,  but  he  understands  nothing  of  his 
art."  (Kousseau,  JZmilius,  vol.  3,  p.  205,  ed* 
1783,  London.) 

132.  In  the  extract  following,  the  Socratic 
Mode,  often  improperly  called  Method,  is  illus- 
trated :  "  Now  a  guide,  when  he  has  found  a 
man  out  of  the  road  leads  him  into  the  right 
way  :  he  does  not  ridicule  or  abuse  him  and 


124  ON  THE  THEORY   OF 

then  leave  him.  Do  you  also  show  the  illiterate 
man  the  truth,  and  you  will  see  that  he  follows. 
But  so  long  as  you  do  not  show  him  the  truth, 
do  not  ridicule  him,  but  rather  feel  your  own 
incapacity.  How  then  did  Socrates  act  ?  He 
used  to  compel  his  adversary  in  disputation  to 
bear  testimony  to  him,  and  he  wanted  no  other 
witness.  Therefore  he  could  say,  *  I  care  not 
for  other  witnesses,  but  I  am  always  satisfied 
with  the  evidence  (testimony)  of  my  adversary, 
and  I  do  not  ask  the  opinion  of  others,  but  only 
the  opinion  of  him  who  is  disputing  with  me.' 
For  he  used  to  make  the  conclusions  drawn 
from  natural  notions  so  plain  that  every  man  saw 
the  contradiction  (if  it  existed)  and  withdrew 
from  it  (thus):  Does  the  envious  man  rejoice  ? 
By  no  means,  but  he  is  rather  pained.  Well,  do 
you  think  that  envy  is  pain  over  evils  ?  and 
what  envy  is  there  of  evils  ?  Therefore  he  made 
his  adversary  say  that  envy  is  pain  over  good 
things.  Well  then,  would  any  man  envy  those 
who  are  nothing  to  him  ?  By  no  means.  Thus 
having  completed  the  notion  and  distinctly 
fixed  it  he  would  go  away  without  saying  to  his 
adversary,  Define  to  me  envy  ;  and  if  the  ad- 
versary had  defined  envy,  he  did  not  say,  You 
have  defined  it  badly,  for  the  terms  of  the  defi- 
nition do  not  correspond  to  the  thing  defined — 
These  are  technical  terms,  and  for  this  reason 
disagreeable  and  hardly  intelligible  to  illiterate 
men,  which  terms  we  (philosophers)  cannot  lay 
aside.  But  that  the  illiterate  man  himself,  who 
follows  the  appearances  presented  to  him,  should 


METHODS   OF   TEACHING.  125 

be  able  to  concede  any  thing  or  reject  it,  we  can 
never  by  the  use  of  these  terms  move  him  to 
do.  Accordingly  being  conscious  of  our  own 
inability,  we  do  not  attempt  the  thing  ;  at  least 
such  of  us  as  have  any  caution  do  not.  But  the 
greater  part  and  the  rash,  when  they  enter  into 
such  disputation,  confuse  themselves  and  con- 
fuse others  ;  and  finally  abusing  their  adver- 
saries and  abused  by  them,  they  walk  away. 

"  Now  this  was  the  first  and  chief  peculiarity 
of  Socrates,  never  to  be  irritated  in  argument, 
never  to  utter  any  thing  abusive,  any  thing  insult- 
ing, but  to  bear  with  abusive  persons  and  to  put 
an  end  to  the  quarrel.  If  you  would  know  what 
great  power  he  had  in  this  way,  read  the  Sym- 
posium of  Xenophon,  and  you  will  see  how  many 
quarrels  he  put  an  end  to.  Hence  with  good 
reason  in  the  poets  also  this  power  is  most  highly 
praised, 

*  Quickly  with  skill  he  settles  great  disputes. ' 
HESIOD,  TJieogony,  v.  87. 

Well  then  ;  the  matter  is  not  now  very  safe, 
and  particularly  at  Rome  ;  for  he  who  attempts 
to  do  it,  must  not  do  it  in  a  corner,  you 'may  be 
sure,  but  must  go  to  a  man  of  consular  rank,  if 
it  so  happen,  or  to  a  rich  man,  and  ask  him, 
Can  you  tell  me,  Sir,  to  whose  care  you  have 
entrusted  your  horses  ? — By  all  means. — Well 
then  ;  can  you  tell  me  to  whom  you  entrust 
your  gold  or  silver  things  or  your  vest- 
ments f  I  don't  entrust  even  these  to  any  one 
indifferently.  Well  ;  your  own  body,  have  you 


126  OST   THE   THEORY   OF 

already  considered  about  entrusting  the  care 
of  it  to  any  person  ? — Certainly. — To  a  man 
of  experience,  I  suppose,  and  one  acquainted  with 
the  aliptic,  or  with  the  healing  art  ? — With- 
out doubt. — Are  these  the  best  things  that  you 
have,  or  do  you  also  possess  something  else 
which  is  better  than  all  these  ? — What  kind  of 
a  thing  do  you  mean  ? — That  I  mean  which 
makes  use  of  these  things,  and  tests  each  of 
them,  and  deliberates. — Is  it  the  soul  that  you 
mean  ? — You  think  right,  for  it  is  the  soul 
that  I  mean. — In  truth  I  do  think  that  the 
soul  is  a  much  better  thing  than  all  the  others 
which  I  possess. — Can  you  then  show  us  in 
what  way  you  have  taken  care  of  the  soul  ?  for 
it  is  not  likely  that  you,  who  are  so  wise  a  man 
and  have  a  reputation  in  the  city,  inconsiderately 
and  carelessly  allow  the  most  valuable  thing  that 
you  possess  to  be  neglected  and  to  perish. — 
Certainly  not. — But  have  you  taken  care  of 
the  soul  yourself  ;  and  have  you  learned  from 
another  to  do  this,  or  have  you  discovered  the 
means  yourself  ? — Next,  if  you  persist  in  troub- 
ling him,  there  is  danger  that  he  may  raise  his 
hands  and  give  you  blows.  I  was  once  myself 
also  an  admirer  of  this  mode  of  instruction  until 
I  fell  into  these  dangers. "  (Epictetus,  Dis- 
courses, chap,  xii.) 

133.  In  the  following  extract  the  conceptions 
of  Mode  and  Manner  of  Teaching  are  not  dis- 
tinguished from  that  of  Methods  of  Teaching. 
"Another  *  peccant  humour  '  which  at  present 
infects  the  body  of  education  is  the  employment 


METHODS   OF  TEACHING.  127 

of  Mechanical  Methods.  These  methods  were 
perhaps  not  at  first  mechanical  ;  they  have  be- 
come so  by  degeneration  in  the  hands  of  merely 
imitative  persons.  If  a  method  is  not  thoroughly 
assimilated  by  the  teacher  so  as  to  become  a  liv- 
ing part  of  his  own  mind,  if  it  does  not  marry 
itself  willingly  to  his  own  thought  and  his  own 
habits,  if  it  is  adopted  as  a  mere  plan  for  saving 
himself  trouble  and  for  escaping  from  his  usual 
amount  of  work,  it  has  a  tendency  to  degenerate 
into  a  kind  of  machine,  into  something  that 
cannot  call  forth  thought  and  mental  activity  from 
his  pupils.  The  essential  requisite  of  a  method 
is  that  it  shall  be  living  and  possess  the  adapta- 
bility of  life,  and  that  it  shall  not  interfere  with 
but  promote  the  spontaneous  interest  which  the 
pupil  may  be  inclined  to  feel  in  his  subject.  But 
our  ancient  and  standing  enemy — routine — is  at 
hand  here  also,  and  is  always  ready  to  turn  the 
best  method  into  a  monotonous  device,  or  a  crank- 
like  exercise  of  activities.  Man  is  by  nature  a 
hunting  animal,  and  the  heuristic  method  in 
teaching  is  ore  of  the  most  potent  for  developing 
the  mental  powers.  But  in  the  degeneration 
which  is  natural  to  all  human  things,  unless  the 
breath  that  created  them  at  first  breathes  through 
them  again,  among  the  destructive  powers  which 
produce  this  degeneration,  there  is  none  -more 
potent  than  the  habit  of  imitation.  Question 
and  answer — from  the  pupil  as  well  as  from  the 
teacher — is  one  of  the  best  ways  of  searching  out 
truth  that  are  given  to  human  faculties.  But  no 
sooner  is  this  perceived  than  some  one  writes  a 


128  O^T   THE   THEORY   OF 

book  on  what  he  calls  this  method,  and  the  life 
is  killed  out  of  the  method  by  the  very  process 
which  seemed  to  preserve  it — it  is  strangled  in 
the  grasp  of  stereotype.  And  there  are  now 
hundreds  of  books,  used  mostly  in  ladies'  schools, 
in  which  this  base-born  plan  is  still  followed,  to 
the  irretrievable  loss  of  those  who  are  subjected 
to  the  process.  An  eminent  Cambridge  mathe- 
matician at  present  trains -all  his  pupils  on  this 
heuristic  method — and  without  book  ;  and  his 
success  at  the  university  as  well  as  in  school  is 
marked  and  solid.  But  if  he  were  to  give  a 
sketch  of  his  method  in  writing,  it  would  be  ig- 
nobly stuck  to  and  slavishly  followed — to  the 
death  of  the  very  method  he  had  been  endeavour- 
ing to  set  forth  and  recommend.  If  we  could 
only  train  all  our  teachers  to  the  use  and  constant 
practice  of  the  heuristic  method,  we  should  make 
them  themselves  more  strong  in  thought  and 
purpose,  more  firm  and  real  in  their  intellectual 
life,  and  more  capable  of  firing  their  pupils  with 
a  single  and  undivided  zeal  for  truth.  .  .  . 
We  are  in  fact  overdone  with  machinery  ;  our 
education  is  choked  by  the  means  we  use  to 
promote  it ;  and  the  informing  spirit  is  too  often 
absent.  .  .  . 

44  ...  Our  mechanical  methods  blind  us  to 
the  necessity  of  seeking  to  analyse  our  subjects  in 
the  fullest  manner,  and  so  to  arrange  the  steps 
that  the  children  may  go  up  with  ease  and  plea- 
sure. We  are  constantly  giving  knowledge 
prematurely  ;  we  are  every  day  anticipating  re- 
sults which  the  child  will  reach  for  himself  ;  and 


METHODS   OF  TEACHING.  129 

all  over  our  pupils  suffer  in  their  brains  from  the 
malady  of  the  day — imperfect  digestion. ' '  (Mei- 
klejohnj  Inaug.  Address,  Bell  Chair,  of  Education, 
pp.  33-36,  1876.) 

134.  The  expressions  "  Methods  of  Nature," 
"Nature's  Methods,"  "  Consult  Nature  for 
Methods  of  Education  and  Teaching, ' '  are  heard 
from  time  to  time.  It  may  be  profitable  to  ex- 
amine this  conception  a  little.  What  is  Nature  ? 
How  does  she  work  ?  Where  shall  we  find  her  ? 
We  find  her  about  us  everywhere,  as  a  wild,  in- 
congruous, heterogeneous,  restless  mass  of  objects 
and  activities.  The  most  natural  things  in  the 
world,  probably,  are  a  swamp  and  barbarism,  for 
they  are  "fresh  from  the  hand  of  Nature." 
The  most  natural  road  across  the  swamp  is  a 
corduroy  road.  The  most  natural  action  of  a 
boy  is  to  kick  another  boy  when  he  dislikes 
him.  The  most  natural  way  to  occupy  land  is 
to  tent  upon  it,  and  by  force  keep  others  away 
from  it,  as  the  nomadic  peoples  do.  The  most 
natural  of  plows  is  the  Asiatic — the  fork  of  a 
tree.  The  most  natural  apple  is  that  which 
grows  from  the  natural  seed,  not  the  welcome 
fruit  of  the  graft.  We  also  say  that  these  works 
of  art,  all  high  art,  are  natural.  What,  then,  is 
Nature  ?  Nature  is  not  simply  the  fact  that  is 
presented  to  man — she  is  not  alone  an  object 
formed  without  the  help  of  man — she  is  not  a 
single  objective  thing  by  itself.  Nature  is  a 
term  for  Capacities  and  Possibilities,  whether 
of  matter  or  of  mind.  We  speak  of  capacities 
of  the  human  mind,  all  of  which  are  natural  ; 


130  OK  THE  THEORY   OF 

and  the  developments  of  them  are  all  natural. 
Nothing  can  be  produced  which  is  outside  of 
the  range  of  possibilities,  and,  hence,  that  is 
outside  of  Nature.  But  by  way  of  distinc- 
tion, those  things  which  man  himself  has  been 
instrumental  in  directing  and  controlling  are 
called  Artificial.  If  the  swamp  and  the  barba- 
rian are  very  natural,  drained  meadows  and  civ- 
ilization are  very  artificial.  Yet  in  all  these 
cases  man  never  can  go  beyond  what  his  own 
natural  powers  can  naturally  do.  No  man  ever 
constructs  a  bridge  or  paints  a  madonna  that  his 
natural  powers  do  not  naturally  accomplish. 
It  is  all  of  Nature,  and  all  natural — just  as  natural 
as  it  was  for  Demosthenes  to  stammer  or,  subse- 
quently, to  move  all  Greece  by  his  eloquence. 
One  man  uses  his  right  hand  familiarly,  another 
his  left,  and  still  another  both  with  equal  facility 
— which  is  the  natural  one  ?  An  Icelander  natu- 
rally resists  cold — an  African  naturally  resists 
heat — an  American  resists  both  heat  and  cold. 
Which  is  the  natural  case  ?  A  honey  bee  gath- 
ers honey  in  temperate  zones,  but,  moved  south- 
ward, ceases — what  is  the  naturalness  in  the 
case  ?  In  these  cases  one  is  just  as  natural  as 
another — they  all  are  so  because  of  native  en- 
dowments, capacities,  or  possibilities.  What  is 
the  most  natural  language  to  speak,  for  a  child, 
English,  French,  or  Italian  ?  ' '  Man,  by  nature, 
is  formed  to  suffer  with  patience,  and  die  in 
peace.  It  is  the  physicians  with  their  prescrip- 
tions, the  philosophers  with  their  precepts,  and 
the  clergy  with  their  prayers  and  exhortations, 


METHODS   OF   TEACHING.  131 

that  have  debased  the  heart  of  man,  and  made 
him  ignorant  how  to  die/'  (Rousseau,  Emilius, 
vol.  1.  p.  47.)  In  the  following,  which  is  the 
natural  stage  of  relationship,  compared  to  that 
now  established  by  law  and  custom  in  the  United 
States  at  the  present  time  ?  "  We  shall  endeavour 
to  establish  the  following  propositions  : — 1 .  That 
the  most  ancient  system  in  which  the  idea  of 
blood-relationship  was  embodied,  was  the  system 
of  kinship  through  females  only.  2.  That  the 
primitive  groups  were,  or  were  assumed  to  be, 
homogeneous.  3.  That  the  system  of  kinship 
through  females  only  tended  to  render  the  exo- 
gamous  groups  heterogeneous,  and  thus  to  super- 
sede the  system  of  capturing  wives.  4.  That 
in  the  advance  from  savagery  the  system  of 
kinship  through  females  only  was  succeeded  by 
a  system  which  acknowledged  kinship  through 
males  also  ;  and  which,  in  most  cases,  passed 
into  a  system  which  acknowledged  kinship 
through  males  only.  5.  That  the  system  of  kin- 
ship through  males  tended  to  rear  up  homoge- 
neous groups,  and  thus  to  restore  the  original 
condition  of  affairs — where  the  exogamous  preju- 
dice survived — as  regards  both  the  practice  of 
capturing  wives  and  the  evolution  of  the  form 
of  capture.  6.  That  a  local  tribe,  under  the 
combined  influence  of  exogamy  and  the  system 
of  female  kinship,  might  attain  a  balance  of  per- 
sons of  different  sexes  regarded  as  being  of 
different  descent,  and  that  thus  its  members  might 
be  able  to  intermarry  with  one  another,  and 
wholly  within  the  tribe,  consistently  with  the 


132  ON   THE   THEORY    OF 

principle  of  exogamy.  7.  That  a  local  tribe, 
having  reached  this  stage  and  grown  proud 
through  success  in  war,  might  decline  intermar- 
riage with  other  local  tribes  and  become  a  caste. 
8.  That  on  kinship  becoming  agnatic,  the  mem- 
bers of  such  a  tribe  might  yield  to  the  universal 
tendency  of  rude  races  to  eponomy,  and  feign 
themselves  to  be  all  derived  from  a  common  an- 
cestor, and  so  become  endogamous.  And  9. 
That  there  is  reason  to  think  that  some  endo- 
gamous tribes  became  endogamous  in  this  same 
manner.  .  .  .  The  earliest  human  groups  can  have 
had  no  idea  of  kinship.  .  .  .  The  idea  must  be  re- 
garded as  a  growth.  ,  .  .  Individuals  had  been 
affiliated  not  to  persons,  but  to  some  group.  .  .  . 
As  distinguished  from  men  of  other  groups, 
they  would  be  the  group-stock,  and  named  after 
the  group.'7  (McLennan,  Primitive  Marriage, 
pp.  118-123,  ed.  1876,  London.) 

135.  The  question  is  really,  not  what  is  nat- 
ural ?  but  what  is  artificial  ?  If  the  word  has 
any  proper  signification  and  scope,  they  must  be 
something  like  this  : — Artificial  things  include 
all  those  products  and  results  which  have  been 
developed  from  the  capacities  and  possibilities  of 
Nature  by  the  direct  agency  of  man.  Under 
this  definition  come  all  that  man  has  ever  done 
in  civilization  and  in  history — Le.,  in  civilization. 
"  Culture  or  Civilization,  taken  in  its  wide  eth- 
nographic sense,  is  that  complex  whole  which  in- 
cludes knowledge,  belief"  (religious  and  other- 
wise), u  art,  morals,  law,  custom,  and  any  other 
capabilities  and  habits  acquired  by  man  as  a  mem- 


METHODS   OF   TEACHING.  133 

berof  society."  (Tylor,  Primitive  Culture,  vol. 
i.,  p.  1,  ed.  1874,  New  York.)  In  so  far  as  the 
faculties  of  the  mind  are  native  to.  the  mind,  they 
are  natural — but  in  so  far  as  they  are  developed 
into  power  by  this  or  that  kind  of  life,  or  by 
this  or  that  branch  of  knowledge,  and  for  this  or 
that  purpose,  the  developed  powers  and  the  re- 
sulting products  of  effort,  although  quite  natural, 
are  known  as  artificial.  Methods  of  Educa- 
tion are  artificial.  Modes  of  Teaching  are  arti- 
ficial, yet,  if  based  upon  principles,  they  are  na- 
turally founded  upon  the  native  powers  of  the 
learning  mind  and  the  subject-matter  to  be  learned. 
This  subject-matter  is  both  natural  and  artificial, 
although  all  produced  by  the  capacities  of  Na- 
ture. Methods  of  Teaching,  being  founded  upon 
the  innate  nature  of  things,  are  natural. 

136.  It  is  also  true  that  the  term  "  natural, " 
as  commonly  understood  when  applied  to  the 
human  conditions,  means  the  general  idea  or  no- 
tion that  people  acquire  as  an  induction  from 
experience.  An  action  is  pronounced  natural  in 
proportion  as  it  approaches  spontaneous  favor 
from  the  greatest  number  of  observers.  In  pro- 
portion as  it  diverges  from  this  it  is  called 
"  affected, "  "  false,"  "  sham,"  "  unnatural/' 
'  i  monstrous. ' '  Still  all  these  phases  of  experi- 
ence and  observation  are  within  the  capacities  of 
Nature,  and  hence  natural.  A  broad  discrimi- 
nation should  be  made  between  the  term  natural 
as  applied  to  one  individual,  and  as  applied  in 
the  sense  of  the  inductive  general  idea.  The 
author  who  can  gather  up  the  sense  of  the 


134  ON   THE   THEORY   OF 

.greatest  number  of  people  into  one  picture  or 
character,  or  trait  of  experience,  is  called  the 
most  life-like  and  natural  in  his  writings.  But 
he  is  no  more  natural  than  the  man  who  stam- 
mers, or  squints,  or  says,  as  the  child,  "  I  be 
going." 

137.  "  But  the  only  distinct  meaning  of  that 
word  (natural)  is,  stated,  fixed,  or  settled;  since 
what  is  natural  as  much  requires  and  presup- 
poses an  intelligent  agent  to  render  it  so,  i.e.  to 
effect  it  continually,  or  at  stated  times,  as  what 
is  supernatural   or  miraculous  does  to  effect  it 
once."     (Butler,  Analogy,  Malcom's  ed.,  1860, 
p.  94.) 

138.  "  According    to  its  derivation,   nature 
(natura — nascitur)  means  that  which  is  born  or 
produced — the  becoming  ;  that  which  has  a  be- 
ginning and  an  end  ;  that  which  has  not  the 
cause  of  its  existence  in  itself,  and  the  cause  of 
which  must  be  sought  in  something  antecedent 
to  and  beyond  itself — that  is,  nature  is  the  phe- 
nomenal,   This  the  word  expresses  in  the  strong- 
est manner.     That  which  begins  to  be,  as  the  nec- 
essary consequence  of  antecedent  conditions,  is 
natural.     The    co-existence,    resemblance,    and 
succession  of  phenomena  constitute  the  order  of 
nature ;  and   the  uniformity  of  these  relations 
among  phenomena  are  the  laws  of  nature.    .    .    . 
The  word  '  nature  '   is  also  employed  to  denote 
the  essential  properties  of  matter,  and  the  vari- 
ous forms  of    energy,    potential  and  kinetic." 
(Cocker,  Theistic   Conception  of  the  World,  pp. 
193-4,  ed.  1875.) 


METHODS   OF  TEACHING.  135 

139.  li  Nature  is  the  aggregate  or  totality  of 
all  material  or  physical  phenomena.     A  Law  of 
Nature  is  the  statement  of  a  certain  uniformity 
observed  in  the  relations  among  phenomena.  The 
laws  of  nature  are  '  simply  expressions  of  phe- 
nomenal uniformities,  having  no  coercive  power 
whatever.'     (Carpenter.) 

140.  "  The  Uniformity  of  the  Order  of  Na- 
ture may  mean  either  '  uniformity  of  co-exist- 
ence '  or  '  uniformity  of  succession. '  l  Uniformity 
of  co-existence  '  means  that  the  same  substances 
must  always  ha  ye  the  same  essential  properties 
and  the  same  permanent  relations  to  other  sub- 
stances.    .     .     .     The  constancy  of  the  course 
of  nature  or  the  uniformity  of  causation  is  not  a 
self-evident  and  necessary  truth.     In  so  far  as  it 
is  a  scientific  truth  it  is  purely  an  induction  from 
experience,   an  experience  which    is  necessarily 
limited,   and  therefore  does  not  warrant  a  uni- 
versal conclusion.     .     .     .     It  is  an  immediate 
fact  of  consciousness  that  the  will  is    a    cause 
which  is  adequate  to  the  production  of  a  diver- 
sity of  effects.     .     .     .     Physical  science  itself 
does  not  teach  that  the  course  of  nature  is  abso- 
lutely uniform.     .      .     .      i  Nature,'   says  Dr. 
Cohn,    of  Breslau,    '  is  an  equation  with    very 
many  unknown  quantities.     It  is  the  work    of 
natural  science  to  determine  the  value  of  these 
quantities.'  "     (Ibid.,  pp.  325-33.) 

141.  "  According  to  its  derivation,   nature 
should  mean  that  which  is  produced  or  born  ; 
but  it  also  means  that  which  produces  or  causes 
to  be  born.     .     .     .     The  term  nature  is  used 


136  OX   THE   THEORY    OF 

sometimes  in  a  wider,  sometimes  in  a  narrower 
extension.  When  employed  in  its  most  exten- 
sive meaning,  it  embraces  the  two  worlds  of 
mind  and  matter.  When  employed  in  its  more 
restricted  signification,  it  is  a  synomym  for  the 
latter  only,  and  is  then  used  in  contradistinction 
to  the  former.  In  the  Greek  philosophy,  .  .  . 
the  word  was  general  in  its  meaning  ;  and  in- 
cluded not  only  the  sciences  of  matter,  but  also 
those  of  mind.  With  us,  the  term  nature  is 
more  vaguely  extensive  than  the  terms  physics, 
physical,  physiology,  or  even  than  the  adjective 
natural ;  whereas,  in  the  philosophy  of  Germany, 
natur  and  its  correlatives,  .  .  .  are,  in  gen- 
eral, expressive  of  the  world  of  matter  in  contrast 
to  the  world  of  intelligence. 

"Nature  as  opposed  to  art,  all  physical 
causes,  all  the  forces  which  belong  to  physical 
beings,  organic  or  inorganic.  The  nature  or  es- 
sence of  any  particular  being  or  class  of  beings, 
that  which  makes  it  what  it  is. 

"  l  The  word  nature  has  been  used  in  two 
senses, — viz.,  actively  and  passively  ;  energetic 
(—  forma  formans),  and  material  (=  forma 
formata).  Tn  the  first  it  signifies  the  inward 
principle  of  whatever  is  requisite  for  the  reality 
of  a  thing  as  existent ;  while  the  essence,  or  es- 
sential property,  signifies  the  inner  principle  of 
all  that  appertains  to  the  possibility  of  a  thing. 
Hence,  in  accurate  language,  we  say  the  essence 
of  a  mathematical  circle  or  geometrical  figure, 
not  the  nature,  because  in  the  conception  of 
forms,  purely  geometrical,  there  is  no  expression 


METHODS   OF   TEACHING.  137 

or  implication  of  their  real  existence.  In  the 
second  or  material  sense  of  the  word  nature,  we 
mean  by  it  the  sum  total  of  all  things,  as  far  as 
they  are  objects  of  our  senses,  and  consequently 
of  possible  experience — the  aggregate  of  phe- 
nomena, whether  existing  for  our  outer  senses,  or 
for  our  inner  sense.  The  doctrine  concerning 
nature,  would  therefore  .  .  be  more  properly 
entitled  phenomenology,  distinguished  into  its 
two  grand  divisions,  somatology  (=  doctrine  of 
the  general  properties  of  bodies  or  material  sub- 
stances), and  psychology.'  (Coleridge.} 

"  '  There  is  no  such  thing  as  what  men  com- 
monly call  the  course  of  nature,  or  the  power  of 
nature.  The  course  of  nature,  truly  and  prop- 
erly speaking,  is  nothing  else  but  the  will  of 
God  producing  certain  effects  in  a  continued, 
regular,  constant,  and  uniform  manner  ;  which 
course  or  manner  of  acting,  being  in  every  move- 
ment perfectly  arbitrary,  is  as  easy  to  be  altered 
at  any  time  as  to  be  preserved.'  (Clarice.) 

"  t  All  things  are  artificial,'  said  Sir  Thomas 
Browne,  '  for  nature  is  the  art  of  God. '  The 
antithesis  of  nature  and  art  is  a  celebrated  doc- 
trine in  the  peripatetic  philosophy.  Natural 
things  are  distinguished  from  artificial,  inasmuch 
as  they  have,  what  the  latter  are  without,  an  in- 
trinsic principle  of  formation.  (Arist.) 

"  Dr.  Reid  said  that  nature  is  the  name  we 
give  to  the  efficient  cause  of  innumerable  effects 
which  fall  daily  under  observation.  But  if  it  be 
asked  what  nature  is  ?  whether  the  first  universal 
cause  or  a  subordinate  one  ?  whether  one  or 


138  ON   THE   THEORY   OF 

many  ?  whether  intelligent  or  unintelligent  ? — 
upon  these  points  we  find  various  conjectures 
and  theories,  but  no  solid  ground  upon  which 
we  can  rest.  And  I  apprehend  the  wisest  men 
are  they  who  are  sensible  that  they  know  noth- 
ing of  the  matter. ' '  (Fleming,  Vocab.  of  Phil. ) 
142.  "  When  he  was  visited  by  one  of  the 
magistrates,  Epictetus  inquired  of  him  about 
several  particulars,  and  asked  if  he  had  children 
and  a  wife.  The  man  replied  that  he  had  ;  and 
Epictetus  inquired  further,  how  he  felt  under 
the  circumstances.  Miserable,  the  man  said. 
Then  Epictetus  asked,  In  what  respect,  for  men 
do  not  marry  in  order  to  be  wretched,  but  rather 
to  be  happy.  But  I,  the  man  replied,  am  so 
wretched  about  my  children  that  lately,  when 
my  little  daughter  was  sick  and  was  supposed 
to  be  in  danger,  I  could  not  endure  to  stay  with 
her,  but  I  left  home  till  a  person  sent  me  news 
that  she  had  recovered.  Well  then,  said  Epic- 
tetus, do  you  think  that  you  acted  right  ?  I 
acted  naturally,  the  man  replied.  But  convince 
me  of  this  that  you  acted  naturally,  and  I  will 
convince  you  that  everything  which  takes  place 
according  to  nature  takes  place  rightly.  This  is 
the  case,  said  the  man,  with  all  or  at  least  most 
fathers.  I  do  not  deny  that.:  but  the  matter 
about  which  we  are  inquiring  is  whether  such  be- 
haviour is  right  ;  for  in  respect  to  this  matter  we 
must  say  that  tumours  also  come  for  the  good 
of  the  body,  because  they  do  come  ;  and  gene- 
rally we  must  say  that  to  do  wrong  is  natural, 
because  nearly  all  or  at  least  most  of  us  do  wrong. 


METHODS   OF   TEACHING.  139 

Do  you  show  me  then  how  your  behaviour  is  nat- 
ural. I  cannot,  he  said  ;  but  do  you  show  me 
how  it  is  not  done  according  to  nature,  and  is 
not  rightly  done."  (Epictetus,  Discourses,  Book 
I.,  Chap.  XL,  Long'0  trans.) 

143.  "  The  object  of  what  we  commonly 
call  education — that  education  in  which  man  in- 
tervenes and  which  I  shall  distinguish  as  artificial 
education — is  to  make  good  these  defects  in 
Nature's  methods  ;  to  prepare  the  child  to  re- 
ceive Nature's  education,  neither  incapably  nor 
ignorantly,  nor  with  wilful  disobedience  ;  and  to 
understand  the  preliminary  symptoms  of  her  dis- 
pleasure, without  waiting  for  the  box  on  the  ear. 
In  short,  all  artificial  education  ought  to  be  an 
anticipation  of  natural  education.  And  a  liberal 
education  is  an  artificial  education,  which  has 
not  only  prepared  a  man  to  escape  the  great  evils 
of  disobedience  to  natural  laws,  but  has  trained 
him  to  appreciate  and  to  seize  upon  the  rewards, 
which  Nature  scatters  with  as  free  a  hand  as  her 
penalties.  .  .  .  Ignorance  is  visited  as 
sharply  as  wilful  disobedience — incapacity  meets 
with  the  same  punishment  as  crime. "  (Huxley, 
Lay  Sermons,  p.  34,  ed.  1870.) 


II. 


ON  THE  PRACTICE  OF  METHODS  OF 
TEACHING. 

(A)    ON    THE    KNOWING    FACULTIES    OF    THE    MIND. 

144.  In  discussing  these  Elements  of  Meth- 
ods of  Teaching,  no  attempt  is  made  to  present 
a  systematic  view  of  Psychology.     To   do  this 
would  require  a  volume  by  itself,  and  must  be 
reserved  for  another  occasion  as  opportunities 
shall  permit.     Sufficient  data  are  introduced  to 
serve  as  bases  for  Methods  of  Teaching.     With- 
out endeavoring  to  classify  the  matter  inserted, 
it  is  used  as  it  best  serves  the  scope  of  the  inves- 
tigation.    This  matter   is  also  very  valuable  to 
the  student  for  its  suggestiveness,  even  when  it 
does  not  bear  directly  upon  the  line  of  the  in- 
quiry.    Those  professional  students,  who  are  al- 
ready familiar  with  some  system  of  Psychology, 
will  need  to  be  delayed  only  a  short  time  on  this 
division  of  the  volume. 

145.  Adapting  from  Sir  William  Hamilton's 
Metaphysics,  Murray's  text,  edition  of  1874,  pp. 
39—66,  psychological  phenomena  of  conscious- 
ness are  classified  under  three  great  divisions  : 
(1)  Cognitions,  or  the  faculties  which  have  the 


OF  THE   MIND.  141 

power  to  know  ;  (2)  Feelings,  or  sensibilities, 
those  which  are  susceptible  of  giving  pain  or 
pleasure  ;  (3)  Conations,  which  are  "  tendencies 
to  action,  and  are  divisible  into  classes,  as  such 
tendencies  are  either  blind  and  fatal,  or  deliberate 
and  free.  The  former  are  desires,  the  latter, 
volitions,  (p.  226).  For  present  purposes  it  is 
necessary  to  elaborate  only  the  first  division, 
cognitions,  including  consciousness. 

146.  (a)  "  Consciousness  is  the  recognition 
by  the  thinking  subject  of  its  own  acts  or  affec- 
tions. It  is  an  actual  and  not  a  potential  knowl- 
edge. It  is  an  immediate,  not  a  mediate  knowl- 
edge. It  supposes  a  contrast,  a  discrimination 
— as  the  ego  and  non-ego,  the  discrimination  of 
states  or  modifications  of  the  internal  subject  or 
self  from  each  other,  and  the  distinction  be- 
tween the  parts  and  qualities  of  the  outer  world. 
It  involves  judgment,  or  the  mental  act  by 
which  one  thing  is  affirmed  or  denied  of  an- 
other. It  is  conditioned  upon  memory,  for 
without  this  our  mental  states  could  not  be  held 
fast,  compared,  distinguished  from  each  other, 
and  referred  to  self.  Consciousness  in  its  sim- 
plicity necessarily  involves  three  things, — (1.)  a 
recognizing  or  knowing  subject,  ego  ;  (2.)  a 
recognized  or  known  modification  ;  and  (3.)  a 
recognition  or  knowledge  by  the  subject  of  the 
modification  (pp.  39-42). 

(b)  "  Comparison  requires  a  tertium  quid,  a 
locus — call  it  what  you  will— in  which  the  two 
QiaiwaJExL  existences  may  meet  on  equal  terms. 
rHubifa»am  is  what  is  known  as  a  consciousness. 


142          ON  THE   KNOWING   FACULTIES 

Even  sensations  cannot  be  supposed,  simply  as 
such,  to  be  aware  of  their  relations  to  each  other. 
A  succession  of  feelings  is  not  (as  James  Mill 
reiterates)  one  and  the  same  thing  with  a  feeling 
of  succession,  but  a  wholly  different  thing.  The 
latter  feeling  requires  a  self -transcendency  of 
each  item,  so  that  each  not  only  is  in  relation, 
but  knows  its  relation,  to  the  other.  This  self- 
transcendency  of  data  constitutes  the  conscious 
form.  Where  we  suppose  it  to  exist  we  have 
mind  ;  where  mind  exists  we  have  it.  ... 
Thus,  then,  tbe  words  Use,  Advantage,  Interest, 
Good,  find  no  application  in  a  world  in  which  no 
consciousness  exists.  Things  there  are  neither 
good  nor  bad  ;  they  simply  are  or  are  not.  Ideal 
truth  to  exist  at  all  requires  that  a  mind  also  ex- 
ist which  shall  deal  with  it  as  a  judge  deals  with 
the  law,  really  creating  that  which  it  professes 
only  to  declare.  .  .  .  This  category  (of 
consciousness,  or  personality)  might  be  defined 
as  the  mode  in  which  data  are  brought  together 
for  comparison  with  a  view  to  choice.  Both 
these  points,  comparison  and  choice,  will  be 
found  alike  omnipresent  in  the  different  stages 
of  its  activity.  The  former  has  always  been  rec- 
ognized ;  the  latter  less  than  it  deserves.  Many 
have  been  the  definitions  given  by  psychologists 
of  the  essence  of  consciousness.  One  of  the  most 
acute  and  emphatic  of  all  is  that  of  Ulrici,  who 
in  his  Leib  und  Seele  and  elsewhere  exactly  re- 
verses the  formula  of  the  reigning  British  school, 
by  calling  consciousness  a  discriminating  activity. 
But  even  Ulrici  does  not  pretend  that  conscious- 


OF  THE  MLNTD.  143 

ness  creates  the  differences  it  becomes  aware  of 
in  its  objects.  They  pre-exist  and  consciousness 
only  discerns  them  ;  so  that  after  all  Ulriei's  defi- 
nition amounts  to  little  more  than  saying  that 
consciousness  is  a  faculty  of  cognition — a  rather 
barren  result.  I  think  we  nia^  go  farther  and 
add  that  the  powers  of  cognition,  discrimination 
and  comparison  which  it  possesses,  exist  only  for 
the  sake  of  something  beyond  themselves,  name- 
ly, Selection.  Whoever  studies  consciousness, 
from  any  point  of  view  whatever,  is  ultimately 
brought  up  against  the  mystery  of  interest  and 
selective  attention.  There  are  a  great  many 
things  which  consciousness  is  in  a  passive  and 
receptive  way  by  its  cognitive  and  registrative 
powers.  But  there  is  one  thing  which  it  does, 
suft  sponte,  and  which  seems  an  original  peculi- 
arity of  its  own  ;  and  that  is,  always  to  choose 
out  of  the  manifold  experiences  present  to  it  at 
a  given  time  some  one  for  particular  accentua- 
tion, and  to  ignore  the  rest.  And  .  .  from  its 
simplest  to  its  most  complicated  forms,  it  exerts 
this  function  with  unremitting  industry. ' '  (James, 
Article  in  Mind,  No.  XIII. ,  January,  1879,  pp. 
6-9.) 

147.  "I.  In  the  first  place,  as  we  are  en- 
dowed with  a  faculty  of  Cognition,  or  Conscious- 
ness in  general,  and  since  it  cannot  be  maintained 
that  we  have  always  possessed  the  knowledge 
which  we  now  possess,  it  will  be  admitted  that 
we  must  have  a  faculty  of  acquiring  knowledge. 
But  this  acquisition  of  knowledge  can  only  be 
accomplished  by  the  immediate  presentation  of  a 


144          OK   THE   KNOWING   FACULTIES 

new  object  to  consciousness  ;  in  other  words,  by 
the  reception  of  a  new  object  within  the  sphere 
of  our  cognition.  We  have  thus  a  faculty  which 
may  be  called  the  Acquisitive,  or  the  Presenta- 
tive,  or  the  Receptive.  Now,  new  or  adventi- 
tious knowledge  may  be  either  of  things  external 
or  of  things  internal.  If  the  object  of  knowledge 
be  external,  the  faculty  receptive  or  presentative 
of  the  qualities  of  such  object  will  be  a  conscious- 
ness of  the  non-ego.  This  has  obtained  the 
name  of  External  Perception,  or  of  Perception 
simply.  If,  on  the  other  hand,  the  object  be 
internal,  the  faculty  receptive  or  presentative  of 
the  qualities  of  such  subject-object,  will  be  a 
consciousness  of  the  ego.  This  faculty  obtains 
the  name  of  Internal  or  Reflex  Perception,  or 
of  Self-consciousness.  By  the  foreign  psychol- 
ogists this  faculty  is  termed  also  the  Internal 
Sense."  (Hamilton.) 

"  The  two  classes  of  sense-perceptions  thus 
characterized  are  the  original  and  the  acquired. 
They  are  thus  defined  :  an  original  perception  is 
one  that  is  performed  by  a  single  sense,  when 
exercised  alone.  Whatever  the  mind  knows  in 
this  way,  either  of  an  object  or  of  its  relations, 
is  known  directly  and  by  an  original  endowment 
of  man.  It  is  a  pure  work  or  operation  of  na- 
ture, and  cannot  be  traced  to  art.  An  acquired 
perception  is  one  which  we  gain  by  experience  or 
exercise.  We  use  the  knowledge  given  directly 
by  one  sense,  as  the  sign  or  evidence  of  the 
knowledge  which  we  might,  but  do  not,  in  this 
particular  case,  gain  by  another. "  (Porter, 


OF  THE   MLtfD.  145 

The  Human  Intellect,  p.  159,  ed.  1869.)     Con- 
tinuing from  Hamilton  : — 

148.  "  II.    In  the  second  place,   inasmuch, 
as  we  are  capable  of  knowledge,  we  must  be  en- 
dowed not  only  with  a  faculty  of  acquiring,  but 
with  a  faculty  of  retaining  or  conserving  it  when 
acquired.     We  have  thus,  as  a  second  necessary 
faculty,  one  that  may  be  called  the  Conserva- 
tive or  Retentive.     This  is  Memory,  strictly  so 
denominated. 

149.  "  III.  But,   in  the  third  place,  if  we 
are  capable  of  knowledge,  it  is  not  enough  that 
we  possess  a  faculty  of  acquiring,   and  a  faculty 
of  retaining  it  in  the  mind,  but  out  of  conscious- 
ness.   We  have  a  reproductive  power.     This  Re- 
productive faculty  is  governed  by  the  laws  which 
regulate  the  succession  of  our    thoughts, — the 
laws,  as  they  are  called,  of  Mental  Association. 
If  these  laws  are  allowed  to  operate  without  the 
intervention  of  the  will,    this    faculty  may  be 
called  Suggestion,  or  Spontaneous  Suggestion ; 
— whereas,  if  applied  under  the  influence  of  the 
will,  it  will  properly  obtain  the  name  of  Remin- 
iscence, or  Recollection.     By  reproduction,  it 
should  be  observed,  that  I  strictly  mean  the  pro- 
cess of  recovering  the  absent  thought  from  un- 
consciousness, and  not  its  representation  in  con- 
sciousness. 

150.  "  IV.  In  the  fourth  place,  as  capable 
of  knowledge,  we  must  not  only  be  endowed  with 
a  presentative,  a  conservative,  and  a  reproductive 
faculty  ;  there  is  required  for  their  consummation 
a  faculty  of  representing  in  consciousness,  and 


146         OK   THE   KKOWIJSTG   FACULTIES 

of  keeping  before  the  mind  the  knowledge  pre- 
sented, retained,  and  reproduced.  We  have  thus 
a  Representative  faculty  ;  and  this  obtains  the 
name  of  Imagination  or  Phantasy. 

151.  "V.   In  the  fifth  place,  all  the  faculties 
we  have  considered  are  only  subsidiary.     They 
acquire,  preserve,  call  out,  and  hold  up,  the  ma- 
terials, for  the  use  of  a  higher  faculty  which  ope- 
rates upon  these  materials,  and  which  we  may 
call    the    Elaborative    or   Discursive   faculty. 
This  faculty  has  only   one   operation, — it  only 
compares.     It  may  startle  you  to  hear  that  the 
highest  function  of  mind  is  nothing  higher  than 
comparison  ;  but,  in  the  end,   I  am  confident  of 
convincing  you  of  the  paradox.     From  this  mere 
act  of  Comparison,  there  are  created  the  intellec- 
tual products  known  as  Collective  Notions,  Ab- 
stractions,   Generalizations,    Judgments,    and 
Reasoning. 

152.  "  VI.  But,  in  the  sixth  and  last  place, 
the  mind  is  not  altogether  indebted  to  experience 
for  the  whole  apparatus  of  its  knowledge.     What 
we  know  by  experience,  without  experience  we 
should  not  have  known  ;  and  as  all  our  experi- 
ence is  contingent,   all  the  knowledge    derived 
from  experience  is  contingent  also.     But  there 
are  cognitions  in  the  mind  which  are  not  contin- 
gent,— which  are  necessary, — which  we  cannot 
but  think, — which  thought  supposes  as  its  funda- 
mental condition.     These  cognitions,  therefore, 
are   not  mere  generalizations  from    experience. 
But  if  not  derived  from  experience,  they  must  be 
native  to  the  mind.     These  native  cognitions  are 


OF  THE   MIND.  147 

the  laws  by  which  the  mind  is  governed  in  its 
operations,  and  which  afford  the  conditions  of  its 
capacity  of  knowledge.  These  necessary  laws, 
or  primary  conditions  of  intelligence,  are  phe- 
nomena of  a  similar  character  ;  and  we  must, 
therefore,  generalize  or  collect  them  into  a  class  ; 
and  on  the  power  possessed  by  the  mind  of  mani- 
festing these  phenomena  we  may  bestow  the  name 
of  the  Regulative  faculty.  (Lect.  on  Metaph., 
XX.) 

153.  "  The  following  is  a  tabular  view  of 
the  distribution  of  the  Special  Faculties  of 
Knowledge. 

COGNITIVE  FACULTIES. 

T    Prpqpntfltivp    jl-  External—  Perception. 

ltlve    la.  Internal—  Self  -consciousness. 
II.  Conservative—Memory. 

III.  Reproductive 


IV.  Representative  —  Imagination  or  Phantasy. 
V.  Elaborative  —  Comparison,  or   the    Faculty  of 

Relations. 
VI.  Regulative  —  Reason  or  Common  Sense.  '  ' 

154.  "  Some  writers  on  education  call  the 
desire  of  intellectual  progression  the  faculty  of 
obtaining  knowledge,  —  that  is  to  say,  they  call 
painting  seeing,  —  or  the  intellectual  powers,  and 
think  of  the  senses  and  the  memory  as  also  exert- 
ing an  educational  influence  ;  or  they  speak  of 
the  development  of  spontaneous  activity,  as  if  the 
will  itself  were  not  such  a  developing  power. 
.  .  The  will  reproduces  itself  only,  and 
acts  only  within,  not  without,  itself  ;  for  external 


148          ON   THE   KNOWING   FACULTIES 

action  is  as  little  the  new  act  of  the  particular  vo- 
lition, as  are  the  words  signifying  it  of  the  par- 
ticular thought.  The  desire  of  mental  progress, 
on  the  contrary,  enlarges  its  world  for  the  recep- 
tion of  new  creatures,  and  is  as  dependent  on  ob- 
jects as  the  pure  will  is  independent  of  them. 
The  will  could  reach  its  ideal,  but  finds  a  strange 
opposition  to  it, — whereas  no  power  stands  op- 
posed to  thought, — but  only  the  difference  be- 
tween its  steps,  and  the  impossibility  of  seeing 
whither  they  reach.  .  .  .  The  mental  desire 
of  advancement  which,  in  a  higher  sense  than 
the  physical,  works  by  means  of,  and  in  ac- 
cordance with,  the  will,  that  is  to  say,  creates 
new  ideas  out  of  old  ideas,  is  the  distinguish- 
ing characteristic  of  man.  No  will  restrains 
the  order  of  a  beast's  actions.  In  our  wak- 
ing moments  we  are  actually  conscious  that 
we  think  ;  in  our  dreams  we  receive,  if  I  may 
so  express  it,  that  consciousness.  In  the  man 
of  genius  the  formation  of  ideas  appears  actually 
creative  ;  in  ordinary  men,  merely  recoil  ective 
and  necessary. "  (Richter,  Levana,  pp.  342-4.) 

155.  "  The  Intelligence  reaches  its  end  ac- 
cording to  a  certain  way,  process,  or  method. 
.     .     .     The  Formal  movements  of  intelligence 
accordingly  fall  under    two    heads,    thus  : — (a) 
Will-power,     (b)  Process  or  Method  of  reaching 
Knowledge. "     (Laurie,  Syn.  of  Lectures,  p.  10, 
ed.  1877.) 

156.  "No  act  of  intelligence  can  be    per- 
formed without  some  determination  of  the  Ego, 
no  act  of  determination  without  some  cognition, 


OF   THE   MIKD. 

and  no  act  of  the  one  or  the  other  without  some 
amount  of  feeling  being  mingled  in  the  process. 
Thus,  while  each  mental  state  may  have  its  dis- 
tinctive characteristics,  there  is  unity  at  the  root 
—the  identical  Ego,  spirit,  Will  (p.  36).  .  .  . 
When,  therefore,  it  is  asked,  What  causes  the 
will  to  effect  one  volition  rather  than  another  ? 
our  answer  is,  Nothing  whatever  !  Of  its  own 
effect,  Will9  in  its  proper  conditions,  is  not  a 
partial,  but  a  full  and  adequate  cause. ' '  (Cocker, 
Theistic  Conception  of  the  World,  p.  391.) 

167.  In  continuation  of  what  has  been  said 
there  is  added  the  following,  adapted  from  Por- 
ter on  the  Imagination  :  "  The  imagination  has 
various  applications,  (a)  The  poetic  imagina- 
tion is  that  creative  power  which  is  employed  for 
the  gratification  of  the  emotional  nature  in  the 
production  of  pictures  more  or  less  elevating  in 
their  associations,  which  are  fixed  and  expressed 
by  means  of  rhythmical  language. 

158.  (b)  "  The  philosophic  imagination  is- 
that  without  which  philosophic  invention  and 
discovery  are  impossible.  To  invent  or  discover, 
is  always  to  recombine.  It  is  to  adjust  in  new 
positions,  objects  or  parts  of  objects  which  have 
never  been  so  connected  before.  The  discoverer 
of  a  new  solution  for  a  problem,  or  a  new  dem- 
onstration for  a  theorem  in  mathematics,  the 
inventor  of  a  new  application  of  a  power  of  na- 
ture already  known,  or  the  discoverer  of  a  power 
not  previously  dreamed  of,  the  discoverer  of  a 
new  argument  to  prove  or  deduce  a  truth  or  a 


150  ON"   THE   KNOWING   FACULTIES 

new  induction  from  facts  already  accepted,  the 
man  who  evolves  a  new  principle  or  a  new  defi- 
nition in  moral  or  political  science — must  all  ana- 
lyze and  recombine  in  the  mind  things,  acts,  or 
events,  with  their  relations,  in  positions  in  which 
they  have  never  been  previously  observed  or 
thought  of.  This  recombination  is  purely  men- 
tal. If  there  be  a  discovery  or  invention,  there 
has  never  before  been  such  a  juxtaposition  of  the 
materials  nor  of  their  parts  in  the  world  of  fact 
or  in  the  thoughts  of  men.  These  objects  and 
parts  are  now  for  the  first  time  brought  together 
in  the  mind — i.e.,  the  imagination  of  the  dis- 
coverer. Every  discovery  is,  in  fact,  a  work  of 
the  creative  imagination.  ...  In  the  com- 
munication of  scientific  truth  there  can  be  no  ques- 
tion that  a  large  measure  of  imagination  is  of 
essential  service.  He  that  would  amply  illus- 
trate, powerfully  defend,  or  effectively  enforce 
the  principles  and  truths  of  science,  is  greatly 
aided  by  a  brilliant  imagination.  This,  of  all 
other  gifts,  delivers  him  from  that  tendency  to  the 
dry  and  abstract,  to  the  general  and  the  remote, 
to  which  the  expounder  of  science  is  continually 
exposed  from  his  familiarity  with  principles 
which  are  strange  to  his  pupils  and  readers,  and 
which  need  to  be  continually  explained  and  illus- 
trated by  fresh  and  various  examples.  The 
philosophic  writer  or  teacher  who  is  gifted  with 
imagination  is  more  likely  to  be  clear  in  state- 
ment, ample  in  illustration,  pertinent  in  his  ap- 
plication and  exciting  in  his  enforcement  of  the 


OF  THE   MIND.  151 

truths  with  which  his  science  is  conversant,  what- 
ever may  be  the  subject-matter  with  which  the 
science  is  concerned. 

159.  "  (c)  The  practical  or  ethical  uses  of 
the  imagination    are    numerous    and    elevated. 
These   are    sufficiently  obvious  from  the  single 
consideration,  that  the  law  of  duty  is  and  must 
be  an  ideal  law  :  for  whether  it  is  or  is  not  ful- 
filled, it  must  precede  the  act  which  reaches  or 
falls  short  of  itself.     Every  ethical  rule  must  be 
a  mental  creation,  an  ideal  formed  by  the  crea- 
tive power,  and  held  before  the  soul  as  a  guide 
and  law. 

160.  "  (d)  The  relation  of  the  imagination  to 
religious  faith  is    interesting    and    important. 
The  objects  of  our  faith,  by  their  very  definition, 
have  never  been  subjected  to  direct  or  intuitive 
knowledge.     Neither  sense-perception  nor  self- 
consciousness,  have  confronted  them  directly  or 
brought  report  of  them.     And  yet  the  imagina- 
tion pictures  these  objects  as  real  and  most  im- 
portant."      (Human  Intellect,  pp.  366-73,  ed. 
1869.) 

161.  "  The  fact  is,  that  the  educated  Native 
mind  requires  hardening.     That   culture  of  the 
imagination,  that  tenderness  for  it,  which  may 
be  necessary  in  the  West,  is  out  of  place  here  ; 
for  this  is  a  society  in  which,  for  centuries  upon 
centuries,   the  imagination  has    run    riot,    and 
much  of  the  intellectual    weakness    and    moral 
evil  which  afflict  it  to   this    moment,   may  be 
traced  to  imagination  having  so  long  usurped  the 
place   of  reason.      What  the  Native  mind  re- 


152          ON  THE   KNOWING   FACULTIES 

quires,  is  stricter  criteria  of  truth  ;  and  I  look 
for  the  happiest  moral  and  intellectual  results 
from  an  increased  devotion  to  those  sciences  by 
which  no  tests  of  truth  are  accepted,  except  the 
most  rigid."  (Maine,  Village  Communities,  pp. 
275-6,  ed.  1876,  Address  to  University  of  Cal- 
cutta, March,  1866.) 

162.  Concerning    the    subject    of   memory 
more  should  be  said,   because    it    is  a    faculty 
which  performs  so  lasting  and  important  a  part 
in  the   existence   of    man.      Various  views    of 
memory  are   expressed    by  writers  who    study 
Psychology  ;  the  prevailing  notion  appears  to  be 
that  it  is  a  faculty  which  retains  and  reproduces 
in  Consciousness  the  mental  products  that  former- 
ly were   there.      Another  view    of    memory  is 
this  :  Memory  is  that  endowment  of  the  Mind  by 
which  it  is  able  to  reproduce  its  previous  modi- 
fications.    "Modification  is  properly  the  bring- 
ing a  thing  into  a  certain  mode  of  existence." 
{Hamilton,  Metaphysics,  Murray,  p.  33.) 

163.  Regarding  the  nature  of  memory  as  a 
factor  in  the  conception  of  teaching,  the  follow- 
ing opinions  are  appended  : — "  With  regard  to 
younger  boys,  he  said,  *  It  is  a  great  mistake  to- 
think  that  they  should  understand  all  they  learn; 
for  God  has  ordered  that  in  youth  the  memory 
should  act  vigorously,  independent  of  the  under- 
standing— whereas  a  man  cannot  usually  recollect 
a  thing  unless  he  understands  it. '  "  (Life  of  Dr. 
Tho.  Arnold,  pp.  133-4,  ed.  1870,  Boston.)  ' 

164.  "  Imagination,    Memory,    and    Hope, 
are  psychologically  one  and  the  same  faculty.   In 


OF  THE   MLNT).  153 

Imagination,  the  presence  of  the  image  is  neces- 
sarily accompanied  by  a  conviction  of  the  possi- 
ble existence  of  the  corresponding  object  in  an 
intuition.  Memory  is  the  presence  of  the  same 
image,  accompanied  by  a  conviction  of  the  fact, 
that  the  object  represented  has  actually  existed 
in  a  past  intuition.  Hope,  in  like  manner,  is 
the  presence  of  the  same  image,  together  with 
an  anticipation,  more  or  less  vivid,  of  the  actual 
existence  of  the  object  in  a  future  intuition. 
Imagination,  memory,  and  hope,  are  thus 
(whether  formed  by  a  reflective  process  or  not)  in 
their  actual  results  partly  presentative,  partly  rep- 
resentative. They  are  presentative  of  the  im- 
age, which  has  its  own  distinct  existence  in  con- 
sciousness, irrespectively  of  its  relation  to  the  ob- 
ject which  it  is  supposed  to  represent.  They 
are  representative  of  the  object,  which  that  im- 
age resembles,  and  which,  either  in  its  present 
form  or  in  its  several  elements,  must  have  been 
presented  in  a  past  act  of  intuition.  Thus  there 
is  combined  an  immediate  consciousness  of  the 
present  with  a  mediate  consciousness  of  the  past. 
An  immediate  or  presentative  consciousness  of 
the  past  or  the  future,  as  such,  is  impossible. 
Imagination,  being  representative  of  an  intuition, 
is,  like  intuition,  only  possible  on  the  condition 
that  its  immediate  object  should  be  an  indi- 
vidual. ...  On  the  other  hand,  my  no- 
tion of  a  man  in  general  can  attain  to  univer- 
sality only  by  surrendering  resemblance  ;  it  be- 
comes the  indifferent  representative  of  all  man- 
kind, only  because  it  has  no  special  likeness  to 


154          ON  THE   KNOWING   FACULTIES 

any  one  in  particular.  This  distinction  must  be 
carefully  borne  in  mind  in  comparing  imagina- 
tion with  the  cognate  process  of  conception. 
Memory  is  sometimes  considered  as  the 
result  of  a  process  of  thought."  (Mansel,  Meta- 
physics,  pp.  128-9,  ed.  1871.) 

165.  "  '  The  resuscitation  of  thoughts  which 
in  some  shape  or  other  have  previously  occupied 
the  mind,'  is  nothing  more  or  less  than  a  prel- 
ude to  what  will  unquestionably  form  a  chief 
part  of  our  intellectual  experience  of  futurity  ; 
namely,  the  inalienable  and  irrepressible  recolleV 
tion  of  the  deeds  and  feelings  played  forth  while 
in  the  flesh,  providing  a  beatitude  or  a  misery 
forever.  Ordinarily,  this  resuscitation  is  of  such 
a  medley  and  jumbled  character,  that  not  only  is 
the  general  product  unintelligible,  but  the  par- 
ticular incidents  are  themselves  too  fragmentary 
and  dislocated  to  be  recognised.  But  it  is  not 
always  so.  There  must  be  few  who  have  not 
experienced  in  their  sleep,  with  what  peculiar 
vividness,  unknown  to  their  waking  hours,  and 
with  what  minute  exactitude  of  portraiture, 
events  long  past  and  long  lost  sight  of,  will  not 
infrequently  come  back,  shewing  that  there  is 
something  within  which  never  forgets,  and  which 
only  waits  the  negation  of  the  external  world,  to 
leap  up  and  certify  its  powers.  .  .  .  That 
which  so  vividly  remembers  is  the  Soul  ;  and  if 
in  the  sleep  which  refreshes  our  organic  nature, 
it  utters  its  recollections  brokenly  and  indistinct- 
ly, it  will  abundantly  compensate  itself  when  the 
material  vesture  which  clogs  it  shall  be  cast 


OF   THE   MIND.  155 

away.  Much  of  the  indistinctness  of  dreams 
probably  arises  from  physical  unhealthiness.  If 
a  sound  body  be  one  of  the  first  requirements  to 
a  sound  mind,  in  relation  to  its  waking  employ- 
ments, no  less  must  it  be  needful  to  the  sanity 
and  precision  of  its  sleeping  ones.  Brilliant  as 
are  the  powers  and  functions  of  the  spiritual 
body,  the  performance  of  them,  whether  sleep- 
ing or  waking,  so  long  as  it  is  investured  with 
flesh  and  blood,  is  immensely,  perhaps  wholly, 
contingent  on  the  health  of  the  material  body. ' ' 
(Grindon,  Life,  pp.  290-291,  3d  ed.,  London.) 

166.  "  Memory,  a  receptive,  not  a  creative 
faculty,  is  subjected  to  physical  conditions  more 
than  all  other  mental  powers  ;  for  every  kind  of 
weakness  (direct  and  indirect,  as  well  bleeding  as 
intoxication)  impairs  it,  and  dreams  interrupt  it ; 
it  is  not  subject  to  the  will,  is  possessed  by  us 
in  common  with  the  beasts  ;  and  can  be  most 
effectually  strengthened  by  the  physician:  a  bit- 
ter stomachic  will  increase  it  more  than  a  whole 
dictionary  learnt  by  heart.  For  if  it  gained 
strength  by  what  it  receives,  it  would  grow  with 
increasing  years,  that  is,  in  proportion  to  its  , 
wealth  in  hoarded  names  ;  but  it  can  carry  the 
heaviest  burdens  most  easily  in  un practiced  youth, 
and  it  holds  those  so  firmly  that  they  appear 
above  the  gray  hairs  of  age  as  the  evergreens  of 
childhood. "  (Richter,  Levana,  pp.  370-1  *)  .  .  . 

"  No  one  has  a  memory  for  everything,  be- 
cause no  one  feels  an  interest  in  everything. 
And  the  physical  powers  set  bounds  even  to  the 
strengthening  influence  of  desire  on  the  memory  > 


156          ON  THE   KNOWING   FACULTIES 

— think  of  that  when  with  children, — for  in- 
stance, if  a  Hebrew  bill  of  exchange  for  a  thou- 
sand pounds  were  promised,  on  condition  of  de- 
manding its  payment  in  the  very  words  of  the 
document,  as  once  read  aloud,  everybody  would 
try  to  remember  them,  but,  unless  he  were  a 
Jew,  the  words  and  the  form  would  fail  him. 
.  .  .  I  myself,  however,  would  not  choosev 
any  of  these  proposed  methods  of  catching  and 
yoking  attention  (artificial  arts  of  memory),  but 
would  adopt  that  of  steady  industry.  I  do  be- 
lieve that  a  rod  would  help  a  creeping  child  to 
walk  better  than  crutches  under  his  arms,  which 
at  first  carry,  but  afterwards  are  carried  by  him. 
Yea  yea,  nay  nay,  are  the  best  double  watch- 
words for  children.  .  .  .  Fear  cripples  the 
memory,  both  by  producing  physical  weakness 
and  mental  irritation  ;  the  frost  of  cold  fear 
chains  every  living  power  which  it  approaches. " 
(Richter,  Levana,  pp.  374-6.) 

167.  "It  is  incomprehensible  to  me,  how 
people  fancy  they  can  teach  children  to  read  or 
write  the  letters  easily  by  pointing  out  their  re- 
semblances, and  laying  before  them  at  once  i  y,  c 
C,  or,  in  writing,  i  r,  h  k,  &c.  The  very  oppo- 
site plan  ought  to  be  pursued  ;  i  should  be 
placed  next  g,  v  next  z,  o  next  r ;  the  contrast, 
like  light  and  shadow,  make  both  prominent  ; 
until  reflected  lights  and  half  shades  can  separate 
them  anew  from  each  other.  The  fast-rooted 
dissimilarities  serve  at  last  to  hold  fast  the  re- 
semblance that  exists  among  them.  So  the  old 
plan  of  teaching  spelling  by  lists  of  words  alpha- 


OF   THE   MIND.  157 

betically  arranged  is  bad,  on  account  of  the  diffi- 
culty of  distinguishing  similar  sounds  ;  whereas 
that  of  classing  together  derivations  from  the 
same  Latin  or  Greek  word  assists  the  remem- 
brance, because  the  radical  word  does  not  alter. ' ' 
(Richter,  Levana,  pp.  375-6.) 

168.  "  There  is  not  a  man  living,  whom  it 
would  so  little  become  to  speak  of  memory  as 
myself,  for  I  have  none  at  all  ;  and  do  not  think 
that  the  world  has  again  another  so  treacherous 
as  mine.     My  other  faculties  are  all  very  ordi- 
nary and  mean  ;  but  in  this  I  think  myself  very 
singular,  and  to  such  a  degree  of  excellence,  that 
(besides  the  inconvenience  I  suffer  by  it,  which 
merits  something)   I  deserve    methinks,   to    be 
famous  for  it.  and  to  have  more  than  a  common 
reputation  :  though,  in  truth  the  necessary  use 
of  memory  considered,  Plato  had  reason  when  he 
calPd  it  a  great  and  powerful  Goddess.     In  my 
country,  when  they  would  decypher  a  man  that 
has  no  sense,  they  say,  such  a  one  has  no  mem- 
ory."    (Montaigne,   Essays,  p.   33,   third   ed., 
London.) 

169.  "  I  am  oblig'd  to  fortune  for  having  so 
oft  assaulted  me  with  the  same  sort  of  weapons  ; 
she  forms  and  fashions  me  by  usance,  hardens 
and  habituates  me  so,  that  I  can  know  within  a 
little  for  how  much  I  shall  be  quit.     For  want 
of  natural  memory,  I  make  one  of  paper  ;  and  as 
any  new  symptom  happens  in  my  disease,  I  set 
it  down  ;  from  whence  it  falls  out,  that  being 
now  almost  past  all  sorts  of  examples,  if  any  as- 
tonishment threaten  me,  tumbling  over  these  lit- 


158          OK   THE    KKOWIXG   FACULTIES 

tie  loose  notes,  as  the  Sibyls  leaves,  I  never  fail 
of  finding  matter  of  consolation  from  some  fa- 
vourable prognostick  in  my  past  experience. " 
(Ibid.,  p.  652.) 

' 1  Memory  is  a  faculty  of  wonderful  use,  and 
without  which  the  judgment  can  very  hardly  per- 
form its  office  :  for  my  part  I  have  none  at  all  : 
what  any  one  will  propose  to  me,  he  must  do  it 
by  parcels,  for  to  answer  a  speech  consisting  of 
several  heads,  I  am  not  able.  I  could  not  re- 
ceive a  commission  by  word  of  mouth,  without 
a  note-book  :  and  when  I  have  a  speech  of  con- 
sequence to  make,  if  it  be  long,  I  am  reduc'd 
to  the  miserable  necessity  of  getting  it  word  for 
word  what  I  am  to  say  by  heart  ;  I  should  other- 
wise have  neither  fashion  nor  assurance,  being 
in  fear  that  my  memory  would  play  me  a  slippery 
trick.  But  this  way  is  no  less  difficult  to  me 
than  the  other.  I  must  have  three  hours  to 
learn  three  verses.  And  besides,  in  a  work  of  a 
man's  own,  the  liberty  and  authority  of  altering 
the  order,  of  changing  a  word,  incessantly  vary- 
ing the  matter,  makes  it  harder  to  stick  in  the 
memory  of  the  author.  The  more  I  mistrust  it, 
the  worse  it  is,  it  serves  me  best  by  chance,  I 
must  negligently  sollicit  it,  for  I  press  it,  'tis  as- 
tonish'd,  and  after  it  once  begins  to  stagger,  the 
more  I  sound  it,  the  more  it  is  perplex  'd  ;  it 
serves  me  at  its  own  hour,  not  at  mine.  And 
the  same  defect  I  find  in  my  memory,  I  find  also 
in  several  other  parts.  I  fly  command,  obliga- 
tion and  constraint.  That  which  I  can  other- 
wise naturally  and  easily  do  :  if  I  impose  it  upon 


OF   THE   MIND.  159 

myself  by  an  express  and  strict  injunction,  I  can- 
not do  it.  Being  once  in  a  place  where  it  is 
looked  upon  as  the  greatest  discourtesie  imagina- 
ble not  to  pledge  those  who  drink  to  you, 
though  I  had  there  all  liberty  allowed  me,  I 
try'd  to  play  the  good  fellow,  out  of  respect  to 
the  ladies  that  were  there,  according  to  the  cus- 
tom of  the  country  ;  but  there  was  sport 
enough,  for  this  threatning  and  preparation,  that 
I  was  to  force  myself  contrary  to  my  custom 
and  inclination,  did  so  stop  my  throat,  that  I 
could  not  swallow  one  drop  ;  and  was  depriv'd 
of  drinking  so  much  as  to  my  meat.  I  found 
myself  gorg'd,  and  my  thirst  quench' d  by  so 
much  drink  as  my  imagination  had  swallow 'd. 
This  effect  is  most  manifest  in  such  as  have  the 
most  vehement  and  powerful  imagination  :  but 
it  is  natural  notwithstanding,  and  there  is  no  one 
that  does  not  in  some  measure  find  it.  They 
offer'd  an  excellent  archer,  condemn 'd  to  dye, 
to  save  his  life,  if  he  would  shew  some  notable 
proof  of  his  art,  but  he  refused  to  try,  fearing 
least  the  too  great  contention  of  his  will  would 
make  him  shoot  wide,  and  that  instead  of  saving 
his  life,  he  should  also  lose  the  reputation  he  had 
got  of  being  a  good  marks-man.  A  man  that 
thinks  of  something  else,  will  not  fail  to  take  over 
and  over  again  the  same  number  and  measure  of 
steps,  even  to  an  inch,  in  the  place  where  he 
walks  :  but  if  he  makes  it  his  business  to  mea- 
sure and  count  thorn,  he  will  find  that  what  he 
did  by  nature  and  accident,  he  cannot  so  exactly 
do  by  design.  My  library,  which  is  of  the  best 


160          ON   THE   KNOWING   FACULTIES 

sort  of  country  libraries,  is  situated  in  a  corner 
of  my  house  ;  if  anything  comes  into  my  head 
that  I  have  a  mind  to  look  on  or  to  write  ;  lest  I 
should  forget  it  in  but  going  cross  the  court,  I 
am  fain  to  commit  it  to  the  memory  of  some 
other.  If  I  venture  in  speaking  to  digress  never 
so  little  from  my  subject,  I  am  infallibly  lost, 
which  is  the  reason  that  I  keep  myself  in  dis- 
course strictly  close.  I  am  forced  to  call  the 
men  that  serve  me  either  by  the  names  of  their 
offices,  or  their  country  ;  for  names  are  very  hard 
for  me  to  remember.  I  can  tell  indeed  that 
there  are  three  syllables,  that  it  has  a  harsh 
sound,  and  that  it  begins  or  ends  with  such  a  let- 
ter, but  that's  all  :  and  if  I  should  live  long,  I 
do  not  think  but  I  should  forget  my  own  name,  as 
some  others  have  done.  Messela  Corvinus,  was 
two  years  without,  any  trace  of  memory,  which 
is  also  said  of  Georgius  Trapezuntius.  For 
my  own  interest,  I  often  meditate  what  a  kind 
of  life  theirs  was,  and  if,  without  this  faculty,  I 
should  have  enough  left  to  support  me  with  any 
manner  of  ease,  and  prying  narrowly  into  it,  I 
fear  that  this  privation,  if  absolute,  destroys  all 
the  other  functions  of  the  soul. 

Plenus  rimarum  sum,  hac  atque  iliac  perfluo. 
Ter.  Eun.  act.  1.  fc.  2. 
"  I'm  full  of  chinks,  and  leak  out  every  way." 

It  has  befall'n  me  more  than  once  to  forget  the 
word  I  had  three  hours  before  given  or  receiv'd, 
and  to  forget  where  I  had  hid  my  purse,  what- 
ever Cicero  is  pleas' d  to  say  :  I  help  myself  to 


OF   THE   MIND.  161 

lose  what  I  have  a  particular  care  to  lock  safe  up, 
'  Memoria  certe  non  modo  philosophiam,  sed  om- 
nis  vita3  usum,  omnesque  artes,  una  maxime  con- 
tinet.' — Cicero.  *  The  memory  is  the  recepta- 
cle and  sheath  of  all  science  ;'  and  therefore 
mine  being  so  treacherous,  if  I  know  little,  I  can- 
not much  complain  ;  I  know  in  general  the  names 
of  the  arts,  and  of  what  they  treat,  but  nothing 
more.  I  turn  over  books,  I  do  not  study  them  ; 
what  I  retain  I  do  not  know  to  be  anothers,  and 
is  only  what  my  judgment  has  made  its  advan- 
tage of  ;  discourses  and  imaginations  in  which  it 
has  been  instructed.  The  author,  place,  words, 
and  other  circumstances,  I  immediately  forget, 
and  am  so  excellent  at  forgetting,  that  I  no  less 
forget  my  own  writings  and  compositions  than 
the  rest.  I  am  very  often  quoted  to  myself,  and 
am  not  aware  of  it  ;  and  whoever  should  enquire 
of  me  where  I  had  the  verses  and  examples  that 
I  have  here  huddled  together,  would  puzzle  me 
to  tell  him,  and  yet  I  have  not  borrow' d  them 
but  from  famous  and  known  authors,  not  satisfy- 
ing myself  that  they  were  rich  ;  if  I  moreover 
had  them  not  from  rich  and  honourable  hands, 
where  there  is  a  concurrence  of  authority  as  well 
as  reason.  It  is  no  great  wonder  if  my  book 
run  the  same  fortune  that  other  books  do,  and  if 
my  memory  lose  what  I  have  writ  as  well  as  what 
I  have  read,  and  what  1  give,  as  well  as  what  I 
receive.  Beside  the  defect  of  memory,  I  have 
others  which  very  much  contribute  to  my  igno- 
rance ;  I  have  a  slow  and  heavy  wit,  the  least 
cloud  stops  its  progress,  so  that,  for  example,  I 


162       o:sr  THE  KNOWING  FACULTIES 

never  proposed  to  it  any  never  so  easie  a  riddle 
that  it  could  find  out.  There  is  not  the  least 
idle  subtility,  that  will  not  gravel  me.  In  games, 
where  wit  is  required,  as  chess,  draughts,  and  the 
like,  I  understand  no  more  but  the  motions  of 
the  men,  without  being  capable  of  anything  of 
design.  I  have  a  slow  and  perplex' d  apprehen- 
sion, but  what  it  once  apprehends,  it  apprehends 
well,  for  the  time  it  retains  it."  (Ibid.,  pp.  404- 
406.) 

170.  "  But  the  objection  which  is  common- 
est, and  which  most  intimately  concerns  us  here, 
is,  that  the  knowledge  communicated  by  the  sub- 
ordinate Colleges  and  verified  by  this  University 
is  worthless,  shallow,  and  superficial.  The 
course  of  the  University  of  Calcutta  is  sometimes 
said  to  be  in  fault,  and  it  is  alleged,  to  use  a 
term  at  once  expressive  and  fashionable,  that  it 
encourages  *  cramming.'  Now  there  are  some 
things  in  our  Calcutta  course,  of  which  I  do  not 
altogether  approve.  But  it  was  settled  after 
long  discussion,  shortly  after  I  became  Vice- 
Chancellor,  and  it  would  be  absurd  to  be  per- 
petually changing  that  which  of  all  things  ought 
to  be  fixed  and  permanent,  on  account  of  small 
defects  which  are,  after  all,  disputable.  I  wish, 
however,  to  say  something  of  the  whole  class  of 
objections  implied  in  that  one  word  *  cram- 
ming. '  If  there  is  anything  in  them,  you  know, 
I  suppose,  that  they  have  a  far  wider  application 
than  their  application  to  this  University.  They 
are  constantly  urged  against  the  numerous  com- 
petitive systems  which  are  growing  up  in  Eng- 


OF   THE   MLSTD.  163 

land,  and  in  particular  against  the  system  under 
which  the  Civil  Service  of  India,  probably  the 
most  powerful  official  body  in  the  world,  is  re- 
cruited, and  will  be  recruited. 

"  The  discredit  which  has  been  successfully 
attached  to  certain  systems  by  this  word  is  a 
good  illustration  of  the  power  of  what  a  famous 
writer  called  dyslogistic  expression,  or,  to  put  it 
more  simply,  of  giving  a  thing  a  bad  name.  And 
here  I  must  say,  that  the  habit  Englishmen  have 
of  importing  into  India  these  common-place  cen- 
sorious opinions  about  systems  and  institutions, 
is  a  great  misfortune  for  the  Natives.  Even  in 
the  mouths  of  Englishmen  who  invented  them, 
they  generally  have  very  little  meaning,  for  they 
are  based  on  a  mere  fragment  of  truth  ;  when 
passed  about  among  the  multitude,  they  have 
still  less  ;  and,  at  last,  when  exported  hither, 
and  repeated  by  the  Natives  in  a  foreign  tongue, 
they  have  simply  no  meaning  at  all. 

"  As  far  as  I  understand  the  word,  it  means 
nothing  more  than  the  rapid  communication  of 
knowledge, — communication,  that  is  to  say,  at 
a  rate  unknown  till  recently.  Some  people,  I 
know,  would  add  something  to  the  definition, 
and  would  say  that  cramming  is  the  rapid  com- 
munication of  superficial  knowledge  ;  but  the 
two  statements  will  generally  be  found  identical, 
and  that  they  mean  by  superficial  knowledge, 
knowledge  which  has  been  rapidly  acquired. 
The  true  point,  the  point  which  really  has  to  be 
proved  is,  whether  knowledge  rapidly  acquired 
is  more  easily  forgotten  than  knowledge 


164          ON   THE   KNOWING   FACULTIES 

has  been  slowly  gained.  The  point  is  one  upon 
which,  to  some  extent,  everybody  can  judge  for 
himself  or  herself.  I  do  not  assert  the  negative, 
but  I  am  rather  surprised  at  the  readiness  with 
which  the  affirmative  has  been  usually  taken  for 
granted  ;  no  doubt,  if  it  be  true,  it  is  a  curious 
psychological  fact,  but  surely  there  are  some  rea- 
sons for  questioning  the  reality.  It  might  plausi- 
bly be  argued  that  knowledge  slowly  acquired, 
has  been  acquired  at  the  cost  of  frequent  inter- 
vals of  inattention  and  forgetfulness.  Now 
everybody  knows  that  inattention  and  forgetful- 
ness  tend  to  become  habits  of  the  mind,  and  it 
might  be  maintained  that  these  habits  would  be 
likely  to  recur,  in  association  with  a  subject  of 
thought,  even  when  that  subject  has  for  once 
been  successfully  mastered.  On  the  other  hand, 
it  might  be  contended  that  knowledge  rapidly 
acquired  has  been  necessarily  acquired  under  a 
certain  strain  and  tension  of  the  mental  faculties, 
and  that  the  effects  of  this  tension  are  not  likely 
to  be  so  readily  lost  and  dissipated. 

"  The  simple  truth  is,  that  under  the  strong 
stimulus  applied  by  that  system  of  examinations 
by  which  the  entrance  to  almost  every  English 
profession  is  now  barred,  there  has  sprung  up  an 
active  demand  for  knowledge  of  a  more  varied 
description  than  was  once  coveted,  and  above 
all,  for  knowledge  rapidly  imbibed  and  mastered. 
To  meet  this  demand,  a  class  of  teachers  has 
sprung  up  who  certainly  produce  remarkable 
results  with  remarkable  rapidity.  I  hear  it  said, 
that  they  are  men  of  a  lower  order  of  mind  and 


OF   THE   MIKD.  165 

accomplishment  than  the  teachers  who  follow 
the  old  methods.  It  may  be  so  ;  but  that  only 
renders  the  probability  greater,  that  some  new 
power  has  been  brought  into  play."  (Maine, 
Village  Communities  and  Miscellanies,  pp. 
282-5,  ed.  1876,  Address  to  Univ.  of  Calcutta, 
March,  1866.) 

171.  "I  have  had  some  opportunity  myself 
of  making  a  comparison,   and  my  judgment  is. 
decidedly  in  favour  of  the  present  system  (of  com- 
petitive examinations).     I  am  aware  that  many 
persons  think  the  matter  is  settled  by  asserting 
that  all  we  do  by  our  examination  system,  is  to 
encourage  cram  ;  but  unfortunately  no  definition 
is  given  of  what  is   reprobated  by  this    much 
employed  word.     It  seems  to  me  that  at  least 
one  very  prominent  tendency  of  the  competitive 
system  is  extremely  valuable  ;    namely,  that  of 
securing  from  the  teacher  attention  to  the  prog- 
ress of  his  pupils    individually."      (Todhunter, 
Conflict  of  Studies,  ed.   1873,  pp.  63-4.) 

172.  u  Fortunately,   too,   for  the  opponents 
of  examination,   an   admirable  '  cry '   has    been 
found.     Examination,  they  say,  leads  to  *  cram, ' 
and   '  cram  '    is  the   destruction   of  true   study. 
People  who  know  nothing  else  about  examination 
know  well  enough  that  it  is  *  cram. '     The  word 
has  all  the  attributes  of  a  perfect  question-beg- 
ging epithet.  It  is  short,  emphatic,  and  happily 
derived  from  a  disagreeable  physical  metaphor. 
Accordingly,  there  is  not  a  respectable  gentleman 
distributing  prizes  to   a  body  of  scholars  at  the 
end  of  the  session,  and  at  a  loss  for  something  to 


166          OK  THE   KKOWLtfG   FACULTIES 

say,  who  does  not  think  of  this  word  '  cram, '  and 
proceed  to  expatiate  on  the  evils  of  the  examina- 
tion-system. 

"  I  intend  in  this  article  to  take  up  the  less 
popular  view  of  the  subject  and  say  what  I  can 
in  favour  of  examinations.  I  wish  to  analyse  the 
meaning  of  the  word  '  cram,'  and  decide,  if 
possible,  whether  it  is  the  baneful  thing  that  so 
many  people  say.  There  is  no  difficulty  in  see- 
ing at  once  that  '  cram  '  means  two  different 
things,  which  I  call  '  good  cram '  and  '  bad 
cram. '  A  candidate,  preparing  for  an  important 
competitive  examination,  may  put  himself  under 
a  tutor  well-skilled  in  preparing  for  that  examina- 
tion. This  tutor  looks  for  success  by  carefully 
directing  the  candidate's  studies  into  the  most 
4  paying '  lines,  and  restricting  them  rigorously 
to  those  lines.  The  training  given  may  be  of  an 
arduous,  thorough  character,  so  that  the  faculties 
of  the  pupil  are  stretched  and  exercised  to  their 
utmost  in  those  lines.  This  would  be  called 
4  cram '  because  it  involves  exclusive  devotion 
to  the  answering  of  certain  examination-papers. 
I  call  it  '  good  cram. ' 

"  '  B#d  cram,'  on  the  other  hand,  consists  in 
temporarily  impressing  upon  the  candidate's  mind 
a  collection  of  facts,  dates,  or  formulae,  held  in  a 
wholly  undigested  state  and  ready  to  be  dis- 
gorged in  the  examination-room  by  an  act  of 
mere  memory.  A  candidate,  unable  to  appre- 
hend the  bearing  of  Euclid's  reasoning  in  the 
first  book  of  his  Elements,  may  learn  the  propo- 
sitions off  by  heart,  diagrams,  letters  and  all,  like 


OF  THE   MISTD.  167 

a  Sunday  scholar  learning  the  collects  and  gos- 
pels. Dates,  rules  of  grammar,  and  the  like, 
may  be  i  crammed '  by  mnemonic  lines,  or  by 
one  of  those  wretched  systems  of  artificial  mem- 
ory, teachers  of  which  are  always  going  about. 
In  such  ways  it  is,  I  believe,  possible  to  give  an- 
swers which  simulate  knowledge,  and  no  more 
prove  true  knowledge,  than  the  chattering  of  a 
parrot  proves  intellect. 

"  1  am  far  from  denying  the  existence  of 
4  bad  cram  '  of  this  character,  but  I  hold  that  it 
can  never  be  advantageously  resorted  to  by  those 
who  are  capable  of  '  good  cram.'  To  learn  a 
proposition  of  Euclid  by  heart  is  far  more  labo- 
rious than  for  a  student  of  moderate  capacity  to 
master  the  nature  of  the  reasoning.  It  is  ob- 
vious that  all  advantages,  even  in  an  examina- 
tional point  of  view,  are  on  the  side  of  real 
knowledge.  The  slightest  lapse  of  memory  in 
the  bad  '  crammer, '  for  instance  the  putting  of 
wrong  letters  in  the  diagram,  will  disclose  the 
simulated  character  of  his  work,  and  the  least 
change  in  the  conditions  of  the  proposition  set 
will  frustrate  his  mnemonic  devices  altogether. 
If  papers  be  set  which  really  can  be  answered  by 
mere  memory,  the  badness  is  in  the  examiners. 

* '  Thorough  blockheads  may  be  driven  to  the 
worst  kind  of  '  cram, '  simply  because  they  can 
do  nothing  better.  Nor  do  the  blockheads  suffer" 
harm  ;  to  exercise  the  memory  is  better  than  to 
leave  the  brain  wholly  at  rest.  Some  qualities 
of  endurance  and  resolution  must  be  called  into 
existence,  before  a  youth  can  go  through  the 


168          ON   THE   KNOWING   FACULTIES 

dreary  work  of  learning  off  by  heart  things  of 
which  he  has  no  comprehension.  Nor  with  ex- 
aminers of  the  least  intelligence  is  there  any  rea- 
son to  fear  that  the  best  directed  '  bad  cram  ' 
will  enable  a  really  stupid  candidate  to  carry  off 
honours  and  appointments  due  to  others.  No 
examination-papers  even  for  junior  candidates 
should  consist  entirely  of  t  book-work,'  such  as 
to  be  answered  by  the  simple  reproduction  of  the 
words  in  a  text-book.  In  every  properly  con- 
ducted examination,  questions  are,  as  a  matter  of 
course,  set  to  test  the  candidate's  power  of  ap- 
plying his  knowledge  to  cases  more  or  less  differ- 
ent from  those  described  in  the  books.  More- 
over good  examiners  always  judge  answers  by 
their  general  style  as  well  as  by  their  contents. 
It  is  really  impossible  that  a  stupid  slovenly  can- 
didate can  by  any  art  of  i  cramming '  be  enabled 
to  produce  the  neat,  brief,  pertinent  essay,  a 
page  or  two  long,  which  wins  marks  from  the 
admiring  examiners. 

"  If  we  may  judge  from  experience,  too,  '  bad 
cram  '  does  not  pay  from  the  tutor's  point  of 
view.  That  this  is  so  we  may  learn  from  the 
fact  that  slow  ignorant  pupils  are  ruthlessly  re- 
jected by  the  great  '  coaches.'  Those  who  have 
their  reputation  and  their  living  to  make  by  the 
-success  of  their  candidates  cannot  afford  to  waste 
their  labor  upon  bad  material.  Thus  it  is  not 
the  stupid  who  go  to  the  i  cramming '  tutors  to 
be  forced  over  the  heads  of  the  clever,  but  it  is 
the  clever  ones  who  go  to  secure  the  highest 
places.  Long  before  the  critical  days  of  the 


OF   THE   MIKD.  169 

official  examination,  the  experienced  '  coach '  se- 
lected his  men  almost  as  carefully  as  if  he  were 
making  up  the  University  boat.  There  is  hardly 
a  University  or  a  College  in  the  kingdom  which 
imposes  any  selective  process  of  the  sort.~  An 
entrance  or  matriculation  examination,  if  it  ex- 
ists at  all,  is  little  better  than  a  sham.  All  com- 
ers are  gladly  received  to  give  more  fees  and  the 
appearance  of  prosperity.  Thus  it  too  often 
happens  that  the  bulk  of  a  college  class  consists 
of  untutored  youths  through  whose  ears  the 
learned  instructions  of  the  professor  pass,  harm- 
lessly it  may  be,  but  uselessly.  Parents  and  the 
public  have  little  idea  how  close  a  resemblance 
there  is  between  teaching  and  writing  on  the 
sands  of  the  sea,  unless  either  there  is  a  distinct 
capacity  for  learning  on  the  part  of  the  pupil,  or 
some  system  of  examination  and  reward  to  force 
the  pupil  to  apply. 

* 4  For  these  and  other  reasons  which  might  be 
urged,  I  do  not  consider  it  worth  while  to  con- 
sider '  bad  cram  '  any  further.  I  pass  on  to  in- 
quire whether  l  good  cram  J  is  an  objectionable 
form  of  education.  The  good  *  cramming  '  tutor 
or  lecturer  is  one  whose  object  is  to  enable  his 
pupils  to  take  a  high  place  in  the  list.  With 
this  object  he  carefully  ascertains  the  scope  of 
the  examination,  scrutinises  past  papers,  and  esti- 
mates in  every  possible  way  the  probable  charac- 
ter of  future  papers.  He  then  trains  his  pupils 
in  each  branch  of  study  with  an  intensity  pro- 
portioned to  the  probability  that  questions  will 
be  asked  in  that  branch.  It  is  too  much  to  as- 


170          OK   THE   KNOWING   FACULTIES 

sume  that  this  training  will  be  superficial.  On 
the  contrary,  though  narrow  it  will  probably  be 
intense  and  deep.  It  will  usually  consist  to  a 
considerable  extent  in  preliminary  examinations 
intended  both  to  test  and  train  the  pupil  in  the 
art  of  writing  answers.  The  great  i  coaches  '  at 
Cambridge  in  former  days  might  be  said  \o  pro- 
ceed by  a  constant  system  of  examination,  oral 
instruction  or  simple  reading  being  subordinate  to 
the  solving  of  innumerable  problems.  The  main 
question  which  I  have  to  discuss,  then,  resolves 
itself  into  this  : — whether  intense  training  direct- 
ed to  the  passing  of  certain  defined  examinations 
constitutes  real  education.  The  popular  op- 
ponents of  l  cram  '  imply  that  it  does  not  ;  I 
maintain  that  it  does. 

'  i  It  happened  that,  just  as  I  was  about  to  write 
this  article,  the  Home  Secretary  presided  at  the 
annual  prize-distribution  in  the  Liverpool  College, 
on  the  22d  December,  1876,  and  took  occasion 
to  make  the  usual  remarks  about  '  cram. '  He  ex- 
pressed with  admirable  clearness  the  prevailing 
complaints  against  examinations,  and  I  shall  there- 
fore take  the  liberty  of  making  his  speech  in 
some  degree  my  text.  l  Examination  is  not  edu- 
cation, '  he  said.  '  You  require  a  great  deal  more 
than  that.  As  well  as  being  examined,  you  must 
be  taught.  ...  In  the  great  scramble  for 
life,  there  is  a  notion  at  the  present  moment  of 
getting  hold  of  as  much  general  superficial  knowl- 
edge as  you  can.  That  to  my  mind  is  a  fatal 
mistake.  On  the  other  hand,  there  is  a  great 
notion  that  if  you  can  get  through  your  examina- 


OF  THE   MISTD.  171 

tion  and  i  cram  up  '  a  subject  very  well,  you  are 
being  educated.  That,  too,  is  a  most  fatal  mis- 
take. There  is  nothing  which  would  delight  me 
so  much,  if  I  were  an  examiner,  as  to  baffle  all 
the  i  cramming '  teachers  whose  pupils  came  be- 
fore me  '  (laughter). 

11  Let  us  consider  what  Mr.  Cross  really  means. 
Examination,  he  says,  is  not  education  ;  we  re- 
quire a  great  deal  more  ;  we  must  be  taught  as 
well  as  be  examined.  With  equal  meaning  I 
might  say,  i  Beef  is  not  dinner  ;  we  want  a  great 
deal  more  ;  we  must  have  potatoes,  bread,  pud- 
ding, and  the  like. '  Nevertheless  beef  is  a  prin- 
cipal part  of  dinner.  Nobody,  I  should  think, 
ever  asserted  or  imagined  that  examination  alone 
was  education,  but  I  nevertheless  hold  that  it  is 
one  of  the  chief  elements  of  an  effective  educa- 
tion. As  Mr.  Cross  himself  said  in  an  earlier 
part  of  his  speech,  '  the  examination  is  a  touch- 
stone and  test  which  shows  the  broad  distinction 
between  good  and  bad.  .  .  .  You  may 
manage  to  scramble  through  your  lessons  in  the 
'  half, '  but  I  will  defy  you  to  get  through  your 
examinations  if  you  do  not  know  the  subjects. ' 

"  Another  remark  of  Mr.  Cross  leads  me  to 
the  main  point  of  the  subject.  He  said — '  It  is 
quite  necessary  in  the  matter  of  teaching  that 
whatever  is  taught  must  be  taught  well,  and  noth- 
ing that  is  taught  well  can  be  taught  in  a  hurry. 
It  must  be  taught  not  simply  for  the  examination, 
but  it  must  sink  into  your  minds,  and  stay  there 
for  life.'  Both  in  this  and  his  other  remarks 
Mr.  Cross  commits  himself  to  the  popular  but 


172          ON  THE   KNOWING   FACULTIES 

wholly  erroneous  notion  that  what  boys  learn  at 
school  and  college  should  be  useful  knowledge 
indelibly  impressed  upon  the  mind,  so  as  to 
stay  there  all  their  lives,  and  be  ready  at  their 
fingers'  ends.  The  real  point  of  the  objections 
to  examination  commonly  is,  that  the  candidate 
learns  things  for  the  examination  only,  which, 
when  it  is  safely  passed,  he  forgets  again  as 
speedily  as  possible.  Mr.  Cross  would  teach  so 
deliberately  and  thoroughly  that  the  very  facts 
taught  could  not  be  forgotten,  but  must  ever  af- 
ter crop  up  in  the  mind  whatever  we  are  doing. 
I  hold  that  remarks  such  as  these  proceed  from  a 
wholly  false  view  of  the  nature  and  purposes  of 
education.  It  is  implied  that  the  mind  in  early 
life  is  to  be  stored  with  the  identical  facts,  and 
bits  of  knowledge  which  are  to  be  used  in  after 
life.  It  is,  in  fact,  Mr.  Cross  and  those  who 
think  with  him,  who  advocate  a  kind  of  '  cram/ 
enduring  it  is  true,  but  still  '  bad  cram. '  The 
true  view  of  education,  on  the  contrary,  is  to 
regard  it  as  a  course  of  training.  The  youth  in 
a  gymnasium  practises  upon  the  horizontal  bar, 
in  order  to  develop  his  muscular  powers  general- 
ly ;  he  does  not  intend  to  go  on  posturing  upon 
Horizontal  bars  all  through  life.  School  is  a  place 
where  the  mental  fibres  are  to  be  exercised, 
trained,  expanded,  developed,  and  strengthened, 
not  *  crammed '  or  loaded  with  4  useful  knowl- 
edge. ' 

"  The  whole  of  a  youth's  subsequent  career  is 
one  long  course  of  technical  *  cramming  '  in  which 
any  quantity  of  useful  facts  are  supplied  to  him 


OF   THE    MIND.  173 

nolens  volens.  The  merchant  gets  his  technical 
knowledge  at  the  clerk's  desk,  the  barrister  in 
the  conveyancer's  offices  or  the  law  courts,  the 
engineer  in  the  workshop  and  the  field.  It  is 
the  very  purpose  of  a  liberal  education,  as  it  is 
correctly  called,  to  develop  and  train  the  plastic 
fibres  of  the  youthful  brain,  so  as  to  prevent  them 
taking  too  early  a  definite  *  set, '  which  will  after- 
wards narrow  and  restrict  the  range  of  acquisition 
and  judgment.  I  will  even  go  so  far  as  to  say 
that  it  is  hardly  desirable  for  the  actual  things 
taught  at  school  to  stay  in  the  mind  for  life. 
The  source  of  error  is  the  failure  to  distinguish 
between  the  form  and  the  matter  of  knowledge, 
between  the  facts  themselves  and  the  manner  in 
which  the  mental  powers  deal  with  facts. 

"  It  is  wonderful  that  Mr.  Cross  and  those  who 
moralise  in  his  strain  do  not  perceive  that  the  ac- 
tual facts  which  a  man  deals  with  in  life  are  infi- 
nite in  number,  and  cannot  be  remembered  in  a 
finite  brain.  The  psychologists,  too,  seem  to  me 
to  be  at  fault  in  this  matter,  for  they  have  not 
sufficiently  drawn  attention  to  the  varying  degrees 
of  duration  required  in  a  well  organised  memory. 
We  commonly  use  the  word  Memory  so  as  to 
cover  the  faculties  of  Retention,  Reproduction 
and  Representation,  as  described  by  Hamilton, 
and  very  little  consideration  will  show  that  in 
different  cases  we  need  the  powers  of  retention, 
of  suggestion  and  of  imagination  in  very  differ- 
'ent  degrees.  In  some  cases  we  require  to  re- 
member a  thing  only  a  few  moments,  or  a  few 
minutes  ;  in  other  cases  a  few  hours  or  days  ;  in 


174  OK   THE    KNOWING    FACULTIES 

yet  other  cases  a  few  weeks  or  months  :  it  is  an 
infinitesimally  small  part  of  all  our  mental  impres- 
sions which  can  be  profitably  remembered  for 
years.  Memory  may  be  too  retentive,  and  facil- 
ity of  forgetting  and  of  driving  out  one  train  of 
ideas  by  a  new  train  is  almost  as  essential  to  a 
well-trained  intellect  as  facility  of  retention. 

4 1  Take  the  case  of  a  barrister  in  full  practice, 
who  deals  with  several  cases  in  a  day.  His  busi- 
ness is  to  acquire  as  rapidly  as  possible  the  facts 
of  the  case  immediately  before  him.  With  the 
powers  of  representation  of  a  well-trained  mind, 
he  holds  these  facts  steadily  before  him,  compar- 
ing them  with  each  other,  discovering  their  re- 
lations, applying  to  them  the  principles  and  rules 
of  law  more  deeply  graven  on  his  memory,  or 
bringing  them  into  connection  with  a  few  of  the 
more  prominent  facts  of  previous  cases  which  he 
happens  to  remember.  For  the  details  of  laws 
and  precedents  he  trusts  to  his  text  writers,  the 
statute  book,  and  his  law  library.  Even  before 
the  case  is  finished  his  mind  has  probably  sifted 
out  the  facts  and  rejected  the  unimportant  ones 
by  the  law  of  obliviscence.  One  case  done  with, 
he  takes  up  a  wholly  new  series  of  facts,  and  so 
from  day  to  day,  and  from  month  to  month, 
the  matter  before  him  is  constantly  changing. 
The  same  remarks  are  even  more  true  of  a  busy 
and  able  administrator  like  Mr.  Cross.  The 
points  which  come  before  him  are  infinite  in  va- 
riety. The  facts  of  each  case  are  rapidly  brought 
to  his  notice  by  subordinates,  by  correspondence, 
by  debates  in  the  House,  by  deputations  and  in- 


OF    THE    MIXD.  175 

terviews,  or  by  newspaper  reports.  Applying 
well-trained  powers  of  judgment  to  the  matter  in 
hand,  he  makes  a  rapid  decision  and  passes  to  the 
next  piece  of  business.  It  would  be  fatal  to  Mr. 
Cross  if  he  were  to  allow  things  to  sink  deep  into 
his  mind  and  stay  there.  There  would  be  no 
difficulty  in  showing  that  in  like  manner,  but  in 
varying  degrees,  the  engineer,  the  physician,  the 
merchant,  even  the  tradesman  or  the  intelligent 
artisan,  deal  every  day  with  various  combina- 
tions of  facts  which  cannot  all  be  stored  up  in 
the  cerebral  framework,  and  certainly  need  not 
be  so. 

"  The  bearing  of  these  considerations  upon 
the  subject  of  examinations  ought  to  be  very 
evident.  For  what  is  '  cram  '  but  the  rapid  ac- 
quisition of  a  series  of  facts,  the  vigorous  getting 
up  of  a  case,  in  order  to  exhibit  well-trained 
powers  of  comprehension,  of  judgment,  before  an 
examiner  ?  The  practised  barrister  '  crams  '  up 
his  i  brief '  (so  called  because,  as  some  suppose, 
made  brief  for  the  purpose)  and  stands  an  ex- 
amination in  it  before  a  judge  and  jury.  The 
candidate  is  not  so  hurried  ;  he  spends  months 
or  it  may  be  two  or  three  years  in  getting  up 
his  differential  calculus  or  his  inorganic  chemis- 
try. It  is  quite  likely  that  when  the  ordeal  is 
passed,  and  the  favourable  verdict  delivered,  he 
will  dismiss  the  equations  and  the  salts  and  com- 
pounds from  his  mind  as  rapidly  as  possible  ;  but 
it  does  not  follow  that  the  useful  effect  of  his 
training  vanishes  at  the  same  time.  If  so,  it  fol- 
lows that  almost  all  the  most  able  and  successful 


176  OK   THE   KNOWING    FACULTIES 

men  of  the  present  day  threw  away  their  pains  at 
school  and  college.  I  suppose  that  no  one  ever 
heard  of  a  differential  equation  solving  a  nice  point 
of  law,  nor  is  it  common  to  hear  Sophocles  and 
Tacitus  quoted  by  a  leading  counsel.  Yet  it  can 
hardly  be  denied  that  our  greatest  barristers  and 
judges  were  trained  in  the  mathematical  sciences, 
or  if  not,  that  their  teachers  thought  the  classics 
a  better  training  ground.  If  things  taught  at 
school  and  college  are  to  stay  in  the  mind  to 
serve  us  in  the  business  of  life,  then  almost  all 
the  higher  education  yet  given  in  this  kingdom 
has  missed  its  mark.  I  come  to  the  conclusion, 
then,  that  well-ordered  education  is  a  severe 
system  of  well-sustained  '  cram.'  .  .  .  We 
cannot  consider  it  the  work  of  teachers  to  make 
philosophers  and  scholars  and  geniuses  of  various- 
sorts  :  these,  like  poets,  are  born  not  made. 
Nor,  as  I  have  shown,  is  it  the  business  of  the 
educator  to  impress  indelibly  upon  the  mind  the 
useful  knowledge  which  is  to  guide  the  pupil 
through  life.  This  would  be  '  cram  '  indeed.  It 
is  the  purpose  of  education  so  to  exercise  the 
faculties  of  mind  that  the  infinitely  various  expe- 
rience of  after-life  may  be  observed  and  reasoned 
upon  to  the  best  effect.  What  is  popularly  con- 
demned as  t  cram  '  is  often  the  best  devised  and 
best  conducted  system  of  training  towards  this 
all-important  end."  (Jevons,  l Cram,'  art.  in 
Mind,  pp.  193-207,  No.  VI.,  April,  1877.) 

173.  "  The  act  of  knowing  is  that  activity  of 
the  mind  by  means  of  which  it  consciously  repro- 
duces in  itself  what  actually  exists.  The  act  of 


OF  THE   MIKD.  177 

knowing  is  partly  immediate  or  outer  and  inner 
.  perception,  partly  mediate  or  thinking.  The 
regulative  laws  (injunctions,  prescriptions)  are 
those  universal  conditions  to  which  the  activity 
of  knowledge  must  conform  in  order  to  attain  to 
the  end  and  aim  of  knowledge/'  (Ueberweg, 
Hist.  Log.  Doct.,  p.  1,  ed.  1871.) 

174.  "Knowledge,    in  the   wider  sense   in 
which  we  here  use  the  word,  comprehends  both 
cognition,  which  rests  on  perception  (and  on  the 
evidence  transmitting  perceptions  of  which  we 
are  ignorant),  and  also  knowledge  in  the  stricter 
sense,  which  is  attained  by  thinking. 

175.  "  The  act  of  knowing,  in  so  far  as  it  is 
the  copying  in  the  human  consciousness  of  the 
essence  of  the  thing,  is  an  after-thinking  of  the 
thoughts  which  the  divine  creative  thinking  has 
built    into    things.      In    action    the    preceding 
thought  determines  what  actually  exists,  but  in 
knowing  the  actual  existence,  in  itself  conform- 
able to  reason,  determines  the  human  thought.7' 
(Ibid.,  p.  2.) 

176.  "  1.    The  objective   existence    to    be 
known  consists  not  merely  of  natural  objects, 
but  also  (as  in  history,  etc.)  of  mental  contents. 
2.  The  mirroring  in  consciousness,  although  re- 
production,  cannot  be  accomplished  without  a 
peculiar  activity  of  the  mind.     3.  The  whole  ac- 
tivity of  the  mind  is  not  exhausted  in  knowledge. 
There  is  besides  the  creative  power  of  the  phan- 
tasy, reforming  and  refining  what  is  given  in  the 
conception,   and  ethical  action."      (Ibid.,    pp. 
2-3.) 


178          OK   THE   KNOWING   FACULTIES 

177.  "Knowledge  of  fact  is  knowledge  by 
onlook  ;  knowledge  inferred  is  knowledge  of  one 
thing  through  means  of  another  ;  knowledge  of 
first  principles  is  knowledge  by  insight  into  truth 
higher  than  fact. ' '      (Calderwood,  Hand  Book, 
Moral  Phil.,  p.  39,  ed.  1879.) 

178.  In    giving     the     difference     between 
Thought,  properly  so  called,  and  other  phenom- 
ena of  the  mind,  I  cannot  do  better  than  to  quote 
the  following  :     "  Every  state  of  consciousness 
necessarily  implies  two  elements  at  least :  a  con- 
scious subject,  and  an  object  of  which  he  is  con- 
scious.    In  every  exercise,  for  example,  of  the 
senses,  we  may  distinguish  the  object  seen,  heard, 
smelt,  touched,  tasted,  from  the  subject  seeing, 
hearing,  smelling,   touching,   tasting.     In  every 
emotion  of  pleasure  or  of  pain,  there  is  a  certain 
affection,     agreeable    or    disagreeable,     existing 
within  me,  and  of  this  affection  I  am  conscious. 
In  every  act  of  volition,  there  takes  place  a  certain 
exercise  of  my  will,  and  I  am  conscious  that  it 
takes  place.      .      .      .     But  to  constitute  an  act 
of  Thought,  more  is  required  than  the  immedi- 
ate relation  of  subject  to  object  in  consciousness. 
Every  one  of  the  above  states  might  exist  in  a 
mind  totally  incapable  of  thought.     Let  us  sup- 
pose, for  example,  a  being,  in  whose  mind  every 
successive    state  of  consciousness  was  forgotten 
as  soon  as  it  had  taken  place.     Every  individual 
object  might  be  presented  to  him  precisely  as  it 
is  to  us.     Animals,  men,  trees,  and  stones,  might 
be  successively  placed  before  his  eyes  ;  pleasure, 
and   pain,  and   anger,  and  fear,  might  alternate 


OF  THE   MIKD.  179 

within  him  ;  but,  as  each  departed,  he  would  re- 
tain no  knowledge  that  it  had  ever  existed,  and 
consequently  no  power  of  comparison  with  simi- 
lar or  dissimilar  objects  of  an  earlier  or  later  con- 
sciousness. He  would  have  no  knowledge  of 
such  objects  as  referred  to  separate  notions ; 
he  could  not  say,  this  which  I  see  is  a  man,  or  a 
horse  ;  this  which  I  feel  is  fear,  or  anger.  He 
would  be  deficient  in  the  distinctive  feature  of 
Thought,  the  concept  or  general  notion  resulting 
from  the  comparison  of  objects.  Hence  arises 
the  important  distinction  between  Intuitions,  in 
which  the  object  is  immediately  related  to  the 
conscious  mind,  and  Thoughts,  in  which  the  ob- 
ject is  mediately  related  through  a  concept 
gained  by  comparison.  .  .  .  By  Intuition 
is  meant  to  include  all  the  products  of  the  per- 
ceptive (external  and  internal)  and  imaginative 
faculties  ;  every  act  of  consciousness,  in  short, 
of  which  the  immediate  object  is  an  individual, 
thing,  act,  or  state  of  mind,  presented  under  the 
condition  of  distinct  existence  in  space  or  time. 
It  is  necessary  to  distinguish  between  the  act  of 
thought  and  its  product — the  former  is  desig- 
nated by  the  term  conception,  the  product  by 
concept,  .  .  .  Intuition  contains  two  ele- 
ments only,  the  subject  and  the  object  standing 
in  present  relation  to  each  other.  Thought  con- 
tains three  elements,  the. thinking  subject,  the 
object  about  which  he  thinks,  and  the  concept 
mediating  between  the  two.  Thus  even  the  ex- 
ercise of  the  senses  upon  present  objects,  in  the 
manner  in  which  it  is  ordinarily  performed  by  a 


180          ON  THE   KNOWING   FACULTIES 

man  of  mature  faculties,  does  not  consist  of  mere 
intuition,  but  is  accompanied  by  an  act  of 
thought.  In  mere  intuition,  all  that  is  simulta- 
neously presented  to  the  sense  appears  as  one 
whole  ;  but  mere  intuition  does  not  distinguish 
its  several  parts  from  each  other  under  this  or 
that  notion.  I  may  see  at  once,  in  a  single  pano- 
rama, a  ship  upon  the  sea,  an  island  lying  be- 
hind it,  and  the  sky  above  it.  To  mere  intui- 
tion this  is  presented  only  in  confusion,  as  a  sin- 
gle object.  To  distinguish  its  constituent  por- 
tions, as  sea  and  land,  ship  and  sky,  requires  a 
comparison  and  classification  of  them  relatively 
to  so  many  separate  concepts  existing  in  the 
mind  ;  and  such  classification  is  an  act  of 
Thought. 

In  every  act  of  Consciousness  the  ultimate  ob- 
ject is  an  individual.  But  in  intuition  this  ob- 
ject is  presented  to  the  mind  directly,  and  does 
not  imply  the  existence,  past  or  present,  of  any- 
thing but  itself  and  the  mind  to  which  it  is  pre- 
sented. In  thought,  on  the  other  hand,  the  in- 
dividual is  represented  by  means  of  a  concept, 
which  contains  certain  attributes  applicable  to 
other  individuals  of  the  same  kind.  This  im- 
plies that  there  have  been  presented  to  the  mind 
prior  objects  of  intuition,  originating  the  con- 
cept or  general  notion  to  which  subsequent  objects 
are  referred.  Hence  arises  another  important 
distinction.  All  intuition  is  direct  and  presen- 
tative  ;  all  thought  is  indirect  and  representative. 
By  representation  are  here  included  the 
concept,  which  is  representative  of  many  indi- 


OF   THE  MIND.  181 

viduals,  and  the  image,  which  is  representative 
of  one.  .  .  .  Perception  is  employed  to  de- 
note all  those  states  of  Consciousness  which  are 
presentative  only,  not  representative.  It  will 
thus  include  all  intuitions  except  those  of  Imagi- 
nation. .  .  .  The  office  of  the  faculty  of 
Imagination,  whose  office  is  the  production  of 
images  representative  of  the  several  phenomena 
of  Perception,  internal  as  well  as  external.  .  .  . 
Imagination,  regarded  as  a  product,  may  be  de- 
fined, the  consciousness  of  an  image  in  the  mind 
resembling  and  representing  an  object  of  intui- 
tion. It  is  thus  at  the  same  time  presentative 
and  representative.  It  is  presentative  of  the 
image  which  has  its  own  distinct  existence  in 
consciousness,  irrespective  of  its  relation  to  the 
object  which  it  is  supposed  to  represent.  It  is 
representative  of  the  object  which  that  image  re- 
sembles ;  and  such  resemblance  is  only  possible 
on  the  condition  that  the  image  be,  like  the  ob- 
ject, individual.  .  .  .  The  distinguishing 
feature  of  a  concept  is,  that  it  cannot  in  itself 
be  depicted  to  sense  or  imagination.  It  is 
not  the  sensible  image  of  one  object,  but  an  in- 
telligible relation  between  many.  A  second  im- 
portant characteristic  of  all  concepts  is,  that  they 
require  to  be  fixed  in  a  representative  sign, 
which  is  language."  (Mansel,  Prolegomena 
Logics  pp.  L>()-6,  ed.  1860.) 

179.  "  In  a  psychological  point  of  view,  to 
enumerate  separate  mental  faculties  and  opera- 
tions, as 'giving  rise  to  the  various  products  of 
thought,  is,  to  say  the  least,  to  encumber  the 


182         OK  THE   KNOWING   FACULTIES 

science  with  unnecessary  and  perplexing  distinc- 
tions. It  will  be  sufficient  to  refer  them  to  the 
single  faculty  of  thought  or  reflection,  the  oper- 
ation of  which  is,  in  all  cases,  comparison,  The 
unit  of  thought  is  always  a  judgment,  based  on  a 
comparison  of  objects  ;  and  the  several  operations 
of  thought  are,  in  ultimate  analysis,  nothing 
more  than  judgments  derived  from  different 
data.  In  order  to  exhibit  this  in  special  in- 
stances, it  will  be  convenient  to  adopt  provision- 
ally the  logical  classification,  and  to  examine  the 
phenomena  of  thought  under  the  several  heads 
of  Conception,  Judgment,  and  Reasoning. " 
(Mansel,  Metaphysics,  pp.  176-7,  ed.  1871,  New 
York.) 

180.  "  In  a  psychological  point  of  view,  to 
enumerate  separate  mental  faculties,  as  giving 
rise  to  the  various  products  of  thought,  is,  to 
say  the  least,  to  encumber  the  science  with  un- 
necessary and  perplexing  distinctions.  It  will 
be  sufficient  to  refer  them  to  the  single  faculty 
of  Thought,  the  operation  of  which  is  in  all 
cases  Comparison  (see  Hamilton,  Lect.  on  Meta- 
physics, Lect.  xxxiv.).  But  the  faculty  of 
Thought,  though  uniform  in  its  own  nature  and 
in  the  manner  of  its  operation,  may  yet  give 
rise  to  different  products,  according  to  the  di- 
versity of  the  materials  upon  which  it  operates  ; 
and  this  difference  forms  the  basis  of  the  classi- 
fication usually  adopted  in  Logic.  Extending 
the  terms  Apprehension  and  Judgment  beyond 
the  region  of  Thought  proper  (into  Psychology), 
it  may  be  laid  down,  as  a  general  canon  of  Psy- 


OF   THE   MIND.  183 

ehology,  that  the  unit  of  consciousness  is  a 
judgment;  in  other  words,  that  every  act  of 
consciousness,  intuitive  or  discursive,  is  com- 
prised in  a  conviction  of  the  presence  of  its  ob- 
ject, either  internally  in  the  mind  or  externally 
in  space.  The  result  of  every  such  act  must 
thus  be  generally  stated  in  the  proposition, 
"  This  is  here."  Consequently,  at  least  with 
reference  to  the  primary  and  spontaneous,  as 
distinguished  from  the  secondary  and  reflex  acts 
of  consciousness,  it  is  more  correct  to  describe 
Apprehension  as  the  analysis  of  Judgments,  than 
Judgment  as  the  synthesis  of  Apprehensions.  In 
a  psychological  point  of  view,  therefore,  it  is  in- 
correct to  describe  Simple  Apprehension  as  the 
first  operation  of  the  mind.  In  one  sense,  in- 
deed, the  relation  of  prior  and  posterior  is  al- 
together out  of  place  :  Chronologically,  inas- 
much as  every  Apprehension  is  simultaneous 
with  a  Judgment,  and  every  Judgment  with 
an  Apprehension  ;  and  logically,  inasmuch  as 
Judgment  cannot  exist  without  Apprehension, 
nor  Apprehension  without  Judgment.  In  an- 
other sense,  however,  we  may  properly  say  that 
Judgment  is  prior  to  Apprehension  ;  meaning 
that  the  subject  and  the  object  are  first  given 
in  their  mutual  relation  to  each  other,  before 
either  of  them  can  itself  become  a  separate 
object  of  attention.  But  when  a  correspond- 
ing division  is  adopted  of  the  operation  of 
Thought,  properly  so  called,  the  same  order  of 
priority  cannot  be  observed.  Every  operation 
of  thought  is  a  judgment,  in  the  psychological 


184          ON   THE    KNOWING    FACULTIES 

sense  of  the  term  ;  but  the  psychological  judg- 
ment must  not  be  confounded  with  the  logical. 
The  former  is  the  judgment  of  a  relation  between 
the  conscious  subject  and  the  immediate  object 
of  consciousness  ;  the  latter  is  the  judgment  of 
a  relation  which  two  objects  of  thought  bear  to 
each  other.  The  former  cannot  be  distinguished 
as  true  or  false,  inasmuch  as  the  object  is  there- 
by only  judged  to  be  present  at  the  moment 
when  we  are  conscious  of  it  as  affecting  us  in  a 
certain  manner  ;  and  this  consciousness  is  nec- 
essarily true.  The  latter  is  true  or  false  accord- 
ing as  the  relations  thought  as  existing  between 
certain  concepts  are  actually  found  in  the  ob- 
jects represented  by  those  concepts  or  not. 
The  logical  judgment  necessarily  contains  two 
concepts  (products  of  thought),  and  hence  must 
be  regarded  as  logically  and  chronologically  pos- 
terior to  the  conception  (act  of  thought),  which 
requires  one  only.  The  psychological  judgment 
is  coeval  with  the  first  act  of  consciousness,  and 
is  implied  in  every  mental  process,  whether  of 
intuition  or  of  thought.  It  cannot,  therefore,  be 
called  prior  or  posterior  to  any  other  mental  op- 
eration, for  there  is  no  mental  operation  in 
which  it  does  not  take  place  ;  but  the  judgments 
of  intuition  are  logically  and  chronologically 
prior  to  the  judgments  of  thought.  Conception 
is  a  psychological  judgment,  but  not  a  logical 
one,  and  is  properly  ranked  as  the  first  operation 
of  Thought,  inasmuch  as  it  is  the  simplest.  .  .  . 
Conceiving  has  been  already  explained  as 
the  individualizing  of  certain  attributes  compre- 


OF   THE   MIND.  185 

bended  in  a  general  notion  and  expressed  in  a  gen- 
eral term  ;  the  representation,  namely,  of  such 
attributes  as  coexisting  in  a  possible  object  of 
intuition.  Language  is,  ...  in  its  earliest 
operations,  a  sign,  not  of  concepts,  but  of  intu- 
itions. Its  earliest  terms  are  employed  tis  the 
proper  names  of  individual  objects.  Conception 
does  not  take  place  till  after  we  have  learned  to  give 
the  same  name  to  various  individuals  presented 
to  us  with  certain  differences  of  attributes,  and 
hence  we  associate  it  with  a  portion  only,  not 
with  the  whole,  of  what  is  presented  in  each. 
This  may  be  distinguished  as  Abstraction,  a 
spontaneous,  though  not  always  a  voluntary  act, 
the  concentration  of  the  mind  on  certain  portions 
only  of  a  given  object  in  relation  to  its  name. 
This  must  not  be  treated .  .  as  a  conscious  process 
of  thought,  being  only  a  preliminary  condition 
to  thinking,  taking  place  in  the  majority  of 
cases  unconsciously,  during  the  gradual  acquisi- 
tion of  speech.  Our  names  thus  gradually  ac- 
quire a  signification,  being  transformed  from 
proper  names  to  appellatives.  Finally,  the  act 
of  conception  consists  in  contemplating  the  at- 
tributes thus  combined  in  the  signification  of  a 
name  as  coexisting,  along  with  individual  fea- 
tures, in  a  possible  object  of  intuition,  and  hence, 
apart  from  the  individual  features,  as  indiffer- 
ently representing  all  such  objects.  This  repre- 
sentative collection  of  attributes,  combined  by 
means  of  a  sign,  is  a  Concept.  .  .  .  As  in 
Conception  a  single  general  notion  is  considered 
in  its  relation  to  a  possible  object  of  intuition, 


186          ON   THE   KNOWING   FACULTIES 

so  in  Judgment  two  such  notions  are  considered 
as  related  to  a  common  object.  When  I  assert 
that  A  is  B,  I  do  not  mean  that  the  attributes 
constituting  the  concept  A  are  identical  with 
those  constituting  the  concept  B, — for  this  is 
only  true  in  identical  judgments, — but  that  the 
object  in  which  the  one  set  of  attributes  is  found 
is  the  same  as  that  in  which  the  other  set  is  found. 
The  common  language  and  common 
thought  of  mankind  assume,  whether  they  ex- 
plain it  or  not,  that  a  certain  smell  and  color 
and  form,  which  are  distinct  attributes,  are  in 
some  way  related,  as  parts  or  qualities,  to  some 
one  thing  which  we  call  a  rose  ;  and  that,  when 
I  assert  that  the  rose  is  fragrant,  I  imply  that 
the  thing  which  affects  in  a  certain  way  my 
power  of  sight  is  in  some  manner  identical  (Iden- 
tity) with  that  which  affects  in  a  certain  way  my 
power  of  smell.  .  .  .  Reasoning  is  the  most 
complex  of  the  three  operations,  as  in  it  two 
concepts  are  determined  to  be  in  a  certain  man- 
ner related  to  each  other,  through  the  medium 
of  their  mutual  relations  to  a  third  concept. 
This  operation  is  therefore  treated  last  in  order. 
The  several  relations  asserted  in  the  premises 
and  deduced  in  the  conclusion,  are  of  the  same 
nature  as  those  implied  in  Judgment. 
It  will  be  sufficient  to  attempt  .  .  a  definition  of 
the  products  of  the  several  acts  of  Thought,  the 
Concept,  the  Judgment,  and  the  Syllogism,  the 
legitimate  objects  of  Formal  Logic.  1.  A  Con- 
cept is  a  collection  of  attributes,  united  by  a 
sign,  and  representing  a  possible  object  of  intui- 


OF  THE   MIND.  187 

tion.  2.  A  Judgment  is  a  combination  of  two 
concepts,  related  to  one  or  more  Common  ob- 
jects of  possible  intuition.  3.  A  Syllogism  is  a 
combination  of  two  judgments,  necessitating  a 
third  judgment  as  the  consequence  of  their  mu- 
tual relation. "  (Mansel,  Prolegomena  Loyica, 
pp.  62-9,  ed.  1860.) 

181.  "  The  mental  powers  employed  in  the 
acquisition  of  knowledge  are  probably  three  in 
number.  They  are  substantially  as  Professor 
Bain  has  stated  them  (Senses  and  Intellect,  2d 
ed.,  pp.  5,  325,  etc.): — 1.  The  Power  of  Discrim- 
ination ;  2.  The  Power  of  Detecting  Identity  ; 
3.  The  Power  of  Retention.  We  exert  the  first 
power  in  every  act  of  perception.  Hardly  can 
we  have  a  sensation  or  feeling  unless  we  discrim- 
inate it  from  something  else  which  preceded. 
Consciousness  would  almost  seem  to  consist  in 
the  break  between  one  state  of  mind  and  the 
next,  just  as  an  induced  current  of  electricity 
arises  from  the  beginning  or  the  ending  of  the 
primary  current.  We  are  always  engaged  in  dis- 
crimination ;  and  the  rudiment  of  thought 
which  exists  in  the  lower  animals  probably  con- 
sists in  their  power  of  feeling  difference  and  be- 
ing agitated  by  it.  Yet  had  we  the  power  of 
discrimination  only,  Science  could  not  be  created. 
To  know  that  one  feeling  differs  from  another 
gives  purely  negative  information.  It  cannot 
teach  us  what  will  happen.  In  such  a  state  of 
intellect  each  sensation  would  stand  out  distinct 
from  every  other  ;  there  would  be  no  tie,  no 
bridge  of  affinity  between  them."  We  want  a 


188          OK  THE   KNOWING   FACULTIES 

unifying  power  by  which  the  present  and  the  fu- 
ture may  be  linked  to  the  past  ;  and  this  seems 
to  be  accomplished  by  a  different  power  of  mind. 
Lord  Bacon  has  pointed  out  that  different  men 
possess  in  very  different  degrees  the  powers  of 
discrimination  and  identification.  It  may  be  said 
indeed  that  discrimination  necessarily  implies 
the  action  of  the  opposite  process  of  identifica- 
tion ;  and  so  it  doubtless  does  in  negative  points. 
But  there  is  a  rare  property  of  mind  which  con- 
sists in  penetrating  the  disguise. of  variety  and 
seizing  the  common  elements  of  sameness  ;  and 
it  is  this  property  which  furnishes  the  true  mea- 
sure of  intellect.  The  name  of l  intellect '  expresses 
the  interlacing  of  the  general  and  the  single,  which 
is  the  peculiar  province  of  mind.  (Max  Miiller, 
Lect.  Sci.  Lang.,  2d  series,  Vol.  II.,  p.  63). 
.  .  Plato  said  of  this  unifying  power,  that  if 
he  met  the  man  who  could  detect  the  one  in  the 
many,  he  would  follow  him  as  a  god. ' '  ( Jevons, 
The  Princ.  of  Science,  pp.  4-5,  ed.  1877.) 

"  LAWS  OF  IDENTITY   AND    DIFFERENCE. 

182.  "  At  the  base  of  all  thought  and  science 
must  lie  the  laws  which  express  the  very  nature 
and  conditions  of  the  discriminating  and  identi- 
fying powers  of  mind.  These  are  the  so-called 
Fundamental  Laws  of  Thought,  usually  stated  as 
follows  : — 

1.  The  Law  of  Identity.     Whatever  is,  is. 

2.  The  Law  of  Contradiction.     A  thing  can- 
not  both  be  and  not  be, 


OF   THE   MIKD.  189 

3.  The  Law  of  Duality.  A  thing  must 
either  be  or  not  be. 

' i  The  first  of  these  statements  may  perhaps  be 
regarded  as  a  description  of  identity  itself,  if  so 
fundamental  a  notion  can  admit  of  description. 
A  thing  at  any  moment  is  perfectly  identical  with 
itself,  and,  if  any  person  were  unaware  of  the 
meaning  of  the  word  i  identity,'  we  could  not 
better  describe  it  than  by  such  an  example. 

"  The  second  law  points  out  that  contradictory 
attributes  can  never  be  joined  together.  The 
same  object  may  vary  in  its  different  parts  ;  here 
it  may  be  black,  and  there  white  ;  at  one  time  it 
may  be  hard  and  at  another  time  soft  ;  but  at 
the  same  time  and  place  an  attribute  cannot  be 
both  present  and  absent.  Aristotle  truly  de- 
scribed this  law  as  the  first  of  all  axioms — one 
of  which  we  need  not  seek  for  any  demonstra- 
tion. All  truths  cannot  be  proved,  otherwise 
there  would  be  an  endless  chain  of  demonstra- 
tion ;  and  it  is  in  self-evident  truths  like  this 
that  we  find  the  simplest  foundations. 

'  '  The  third  of  these  laws  completes  the  other 
two.  It  asserts  that  at  every  step  there  are  two 
possible  alternatives — presence  or  absence,  affir- 
mation or  negation.  Hence  I  propose  to  name 
this  law  the  Law  of  Duality,  for  it  gives  to  all 
the  formulae  of  reasoning  a  dual  character.  It 
asserts  also  that  between  presence  and  absence, 
existence  and  non-existence,  affirmation  and  ne- 
gation, there  is  no  third  alternative.  As  Aris- 
totle said,  there. can  be  no  mean  between  oppo- 


190          OK   THE    KNOWING    FACULTIES 

site  assertions  :  we  must  either  affirm  or  deny." 
(Ibid.,  pp.  5-6.) 

183.  "  The  primitive  and  essential  gradation 
of  thought  we  have  indicated  to  be  the  Judg- 
ment. In  accordance  with  what  has  been  said, 
a  Judgment  may  be  denned  to  be  a  recogni- 
tion of  the  identity  or  non-identity  between 
any  two  objects  presented  to  the  Faculty  of 
Thought,  As  expressed  in  words,  a  Judgment 
is  called  a  Proposition,  or  in  grammatical  no- 
menclature, a  Sentence. 

"  Besides  the  Judgment,  there  are  two  other 
products  of  thought,  both  derivatives  from  the 
Judgment.  The  one  is  the  Concept,  which  is 
derived  from  several  Judgments  by  an  act  of 
Conceiving — taking  together,  in  other  words, 
by  an  act  of  synthesis.  The  other  is  the  Rea- 
soning, which  is  derived  from  one  or  more  Judg- 
ments by  an  act  of  analysis  or  separation.  As 
all  thought  is  essentially  a  movement  in  Quan- 
tity, and  as  variations  in  Quantity  can  be  affected 
only  in  the  one  or  the  other  of  these  two  direc- 
tions, synthesis  and  analysis,  the  Concept  and 
the  Reasoning  are  the  only  conceivable  deriva- 
tives from  a  Judgment,  except  such  as  consist 
only  in  variations  of  form,  that  do  not  affect 
the  identity  of  the  thought. 

' i  In  explication  of  this  definition  of  a  Judg- 
ment, it  will  be  necessary  simply  to  recall  what 
has  been  already  said  in  the  exposition  of  the- 
general  nature  of  thought.  As  we  have  seen, 
a  judgment  necessarily  supposes  two  objects  ; 


OF   THE   MIND.  191 

and  its  essential  characteristic,  as  an  act  of  In- 
telligence, consists  in  this  :  that  it  is  a  cognition 
of  this  particular  relation  of  identity  or  non- 
identity  between  the  two  objects.  These  two 
objects  of  a  judgment  are  given  to  it  by  some 
other  faculty  of  the  Intelligence,  as  of  Percep- 
tion, Intuition-,  Memory,  or  by  the  Discursive 
Faculty  itself,  in  some  previous  exercise.  It 
may  be  some  object  of  Perception,  as  Bucephalus. 
As  thus  given  by  the  Perceptive  Faculty,  the 
cognition  is  of  an  object  by  itself,  without  rela- 
tion either  to  other  objects  or  to  the  parts  of 
the  object  itself.  Color  is  not  in  the  percep- 
tion itself  distinguished  from  figure  ;  neither 
color  nor  figure  from  the  position  or  the  time 
in  which  it  is  perceived  ;  and  neither  of 
these  from  the  useful  qualities  of  the  object. 
All  the  perceptible  qualities  are  given  together 
without  distinction  in  the  presentation  itself 
of  the  object.  But  when  thus  given,  the 
mind  at  once,  and  by  a  kind  of  necessity  of  its 
being  as  essentially  active  and  reflective,  exerts 
its  activity  on  it,  first,  by  apprehending  it  as 
a  part  of  a  multiplicity  of  objects  around, 
to  each  of  which  it  stands  in  relation,  and  also, 
as  a  whole,  containing  parts  in  itself.  This  is 
the  primitive  and  conditional  gradation  in  all 
thought — the  apprehension  of  an  object  as  a  part 
or  as  a  whole — in  other  words,  in  the  relation  of 
Quantity.  Simultaneously  with  this,  it  appre- 
hends some  other  object  of  thought  given  to  it 
by  Perception,  or  by  some  other  Faculty  of  the 
Intelligence,  or  in  some  previous  exercise  of  the 


192          OK  THE   KISTOWIKG   FACULTIES 

Judgment,  and  thus  comes  to  view  the  two  ob- 
jects thus  given  in  relation  to  each  other,  as  the 
same  or  not  the  same.  Its  act  then  becomes 
complete  ;  and  a  perfected  product  of  thought, 
a  Judgment,  is  the  result.  Thus  the  second  ob- 
ject may  be  given  in  the  Perception  itself,  as 
black,  or  four-footed,  and  the  Judgment  recog- 
nizes this  color  or  this  form  as  belonging  to 
Bucephalus — that  is,  as  identical  with  one  of  the 
parts  or  characters  that  make  up  the  whole  per- 
ception. Or  the  second  object  may  be  given  by 
the  Regulative  Faculty,  or  Faculty  of  Intuition, 
as  of  Being,  of  Space,  of  Time,  or  other  idea  of 
the  proper  Reason  ;  and  then  the  Judgment  iden- 
tifies Bucephalus  with  Existence,  with  some  part 
of  Space,  of  Time  ;  or  in  other  words,  affirms 
Bucephalus  to  be,  to  be  in  such  a  place,  at 
such  a  time,  and  the  like.  The  second  object 
of  thought  may,  in  like  manner,  be  given  to  the 
Judging  Faculty  by  the  Memory.  We  may 
identify  Bucephalus  as  now  perceived  with  the 
Bucephalus  perceived  yesterday  ;  with  the  black 
color,  the  four-footed  figure,  before  perceived  in 
some  other  object. 

"  The  essential  nature  of  a  Judgment,  thus, 
is  seen  to  be  an  identification  of  one  object 
with  another,  either  totally  or  partially — in  some 
one  or  in  all  respects.  It  is  accordingly  a  rela- 
tive cognition  ;  and  in  the  relation  which  it  in- 
volves are  necessarily  contained  three  elements  : 
1.  The  object  of  thought  identified  with  some 
other.  2.  The  object  with  which  it  is  identi- 
fied, either  in  whole  or  in  part.  And,  3.  The 


OF  THE   MLffD.  19*3 

mental  act  which  identifies.  The  first  two  con- 
stitute the  matter  of  thought,  the  datum ;  the 
last  is  the  Thought  itself,  the  identifying  cogni- 
tion— the  Judgment. 

"  To  the  several  parts,  or  to  different  aspects 
of  the  complex  procedure  in  all  Thought  as 
thus  exemplified  in  one  of  its  gradations — the 
Judgment — Psychology  has  assigned  distinctive 
names,  which  it  may  not  be  inexpedient  here  to 
recall.  Inasmuch  as  the  original  datum  or  ob- 
ject of  thought  is  given  in  an  indefinite  vagueness 
as  one  and  undivided,  and  as,  in  order  to  be 
cognized  in  thought,  it  must  be  viewed  in  rela- 
tion to  some  part,  it  becomes  necessary  to  loosen 
up,  to  analyze  or  separate  it  as  a  whole  into  its 
parts.  This  part  of  the  process  is  called  Analy- 
sis. 

"  The  next  step  is  to  select  the  part  out  of 
the  whole  for  separate  apprehension,  and  to 
draw  it  away,  as  it  were,  to  abstract  it  from  the 
other  parts.  This  part  of  the  movement  in 
Thought  is  called  Abstraction.  The  term,  how- 
ever, it  is  proper  to  add,  is  applied  in  various 
ways  by  different  writers  or  on  different  occasions, 
but  with  the  same  result.  Thus  it  may  be  ap- 
plied to  the  mind  itself  ;  so  that  in  Abstraction 
the  mind,  when  confining  its  view  to  certain 
parts  of  an  object,  is  regarded  as  being  abstracted 
or  drawn  away  from  tie  parts  that  are  to  be  ex- 
cluded from  view  ;  and  this,  it  may  be  observed, 
is  in  strictness  the  most  correct  view.  But  in  a 
looser  sense  the  term  may  be  applied  to  the  part 
itself  that  is  selected,  and  then  such  part  is  re- 


194          ON   THE    KNOWING   FACULTIES 

garded  as  being  abstracted  from  the  other  parts. 
Or,  in  the  third  place,  it  may  be  applied  to 
those  other  excluded  parts  themselves,  and  then 
they  are  regarded  as  being  abstracted  or  drawn 
away  either  from  the  other  parts  or  from  the 
mind's  consideration.  The  result  is  the  same 
in  any  view,  that  one  part  is  separated  from  the 
other  parts  for  exclusive  consideration,  and  it  is 
therefore  a  matter  ot  indifference,  so  far  as  the 
result  is  concerned,  which  of  these  different 
views  is  entertained. 

"  When  thus  one  part  is  separated  from  the 
rest  for  exclusive  consideration  by  the  mind,  the 
act  of  mind  in  which  it  concentrates  its  notice 
upon  it  is  called  Attention. 

"  In  the  next  place,  the  two  objects  are 
brought  up  and  viewed  face  to  face  with  each 
other  in  order  that  their  identity  or  non-identity 
may  be  apprehended.  This  part  of  the  process 
is  called  Comparison, 

"  Finally,  the  last  part  of  the  complex  pro- 
cess, in  which  the  thought  is  perfected  by  bring- 
ing together  the  two  objects  attended  to  into  one 
relative  cognition,  is  called  an  act  of  Synthesis. 

1  i  All  Thought  thus  begins  with  an  Analysis, 
it  proceeds  by  Abstraction,  Attention,  and  Com- 
parison, it  ends  with  a  Synthesis.  And  this  is 
to  be  understood  in  a  sense  more  or  less  full 
and  complete,  in  modes  varying  with  the  nature 
of  the  particular  gradation  of  all  the  acts  of 
thought,  whether  in  judging,  conceiving,  or 
reasoning.  The  two  essential  elements  of  thought 
are  analysis  and  synthesis.  With  one  it  neces- 


OF   THE   MIND.  195 

sarily  begins,  with  the  other  it  necessarily  ends. 
For  its  very  function  is  to  lead  to  truth,  to  a 
unity  in  the  intelligence,  which  supposes  an  un- 
distinguished manifold  as  its  condition,  and  a 
gathering  into  a  unity  as  its  result.  The  other 
parts  of  the  complex  process,  abstraction,  atten- 
tion, and  comparison,  are  the  means  by  which 
the  mind  passes  from  the  multiform  given  in  the 
analysis  to  the  unity  in  the  synthesis. 

"  Of  the  two  objects  of  thought  identified  in 
a  Judgment,  one  is  necessarily  viewed  as  the 
primitive  which  is  to  be  identified  with  the  other, 
or  is  determined  by  it.  This  so  viewed  primi- 
tive or  determined  object  is  called  the  Subject ; 
which  may  be  defined  to  be  that  of  which  we 
judge.  The  other,  viewed  as  the  determining 
element,  is  called  the  Predicate,  which  may  be 
defined  to  be  that  which  is  judged  of  the  subject. 
The  Subject  and  the  Predicate  make  up  the  mat- 
ter of  thought  or  the  datum  to  thought.  They 
are  called  the  Terms  of  a  Proposition  (termini). 
The  act  of  thought  itself  which  recognizes  the 
identity  between  the  two  terms  is  called  the 
Copula,  which  may  be  defined  to  be  the  identifi- 
cation of  two  objects  of  thought.  It  was  called 
by  Aristotle,  in  reference  to  the  two  terms,  an 
Interval."  (Day,  Me.  of  Logic,  pp.  31-5,  ed. 
1868.) 

184.  "  The  Second  gradation  of  Thought  is 
the  Concept.  It  is  derived  from  the  primitive 
product,  the  Judgment,  by  an  act  of  synthesis 
or  composition.  It  accordingly  presupposes  two 
or  more  Judgments,  and,  if  a  valid  product  of 


196          ON   THE   KNOWING   FACULTIES' 

Thought,  can  always  be  resolved  back  into  them. 
It  can,  in  fact,  be  verified  only  by  being  thus  re- 
ferred back  to  the  Judgments  from  which  it  is 
derived.  It  is  formed  either  by  the  synthesis  of 
the  Subjects  of  two  or  more  Judgments,  or  by 
a  synthesis  of  their  Predicates — an  alternative 
which  gives  rise  to  the  two  fundamental  classes 
of  Concepts.  It  may  conduce  to  clearness  to 
exemplify  the  process  of  forming  the  Concept  in 
these  two  ways  separately. 

"  First,  then,  if  we  synthesize  the  subjects, 
the  procedure  will  be  as  follows  :  The  Judg- 
ments, out  of  which  the  Concept  is  to  be  formed, 
we  will  assume  to  be — Socrates  is  rational; 
Cicero  is  rational;  James  is  rational.  By 
uniting  the  subjects,  we  have  Socrates  and  Cicero 
and  James,  and  marking  the  union  by  a  single 
term  which  shall  embrace  them  all  in  one,  we 
will  say,  man,  we  have  the  union  signalized  in 
language.  This  union  of  the  differing  subjects 
of  several  propositions  having  a  common  predi- 
cate is  called  a  Concept ;  in  this  case  a  Concept 
in  Extensive  Quantity.  The  formula  for  the 
formation  of  all  Concepts  of  this  class  is,  accord- 
ingly :  The  Judgments,  B  is  A,  C  is  A,  give  the 
Concept  (B  +  C),  or  when  signalized  in  language 
by  one  term,  the  Concept  D  ;  or  in  brief  :  The 
Judgments  B  is  A,  C  is  A,  give  B  +  C  =  the  Con- 
cept D. 

"  The  procedure  in  forming  Concepts  of  the 
other  class  is  analogous.  Here  the  Subject  re- 
mains the  same,  and  the  Concept  arises  from  the 
synthesis  of  the  Predicates  which  differ.  Thus, 


OF   THE   MIKD.  19? 

the  Predicates  in  the  Judgments,  Socrates  is  ra- 
tional, Socrates  is  animal,  being  united,  we  have 
rational  and  animal,  or  signalizing  the  union  -/ 
by  a  single  term,  we  have  the  Concept,  Man. 
The  term  Man  here,  it  will  be  observed,  means 
a  complement  of  attributes,  as  rational,  animal, 
not,  as  before,  of  subjects,  as  Socrates,  &c. 
This  is  a  concept  in  Comprehensive  Quantity  ; 
the  formula  of  which  is  :  The  Judgments  A  is 
B,  A  is  C,  give,  by  synthesis  of  the  differing 
Predicates,  the  aggregate  (B  +  C),  which  signal- 
ized as  one  in  Language  is  expressed  by  D.  Or 
the  Judgments  A  is  B,  A  is  C,  give  Concept 
(B  +  C)  =  D. 

' '  A  Concept  may  be  defined,  accordingly,  to 
be  a  product  of  Thought,  resulting  from  the 
synthesis  of  the  Subjects  or  of  the  Predicates  in 
several  Judgments. 

"  The  common  Subject  in  a  Predicate-Con- 
cept, or  the  common  Predicate  in  a  Subject- 
Concept,  on  which  the  Concept  is  formed,  is 
called  its  Base. 

"  The  name,  Concept,  is  derived  from  the 
Latin  word  Conception,  meaning  something 
taken  with  another.  The  corresponding  word 
used  to  denote  the  act  of  forming  a  Concept  is 
Conception,  which  is  also  in  common  discourse 
often  used  to  denote  the  product.  It  is  used, 
in  fact,  like  other  words  of  this  kind,  in  the  three- 
fold import  of  faculty,  act,  and  product. 

"  The  Law  of  Identity,  or  as,  in  its  fuller 
expression,  it  may  be  denominated,  the  Law  of 
the  Same  and  Different,  it  will  have  been  seen, 


198         ON   THE   KNOWING   FACULTIES 

presides  over  this  product  of  Thought,  as  over 
the  Judgment.  No  valid  Concept  can  be  formed, 
unless  from  Judgments  which  have  either  iden- 
tical subjects  or  identical  predicates.  The  Con- 
cept arises  from  the  Synthesis  of  the  different 
under  the  same  ;  of  different  subjects  having 
the  same  predicate,  or  of  different  predicates 
having  the  same  subject.  In  other  words,  in  the 
Base  is  to  be  found  the  identifying  principle 
governing  in  the  Concept. 

"  It  will  have  been  observed,  moreover,  from 
the  mode  of  its  formation  that  a  Concept  is  es- 
sentially a  relative  cognition.  It  is  not  only 
the  result  of  a  synthesis,  not  only  the  aggregate 
of  a  plurality  of  Judgments,  and  accordingly  of 
relative  cognitions,  but  the  cognitions  that  are 
brought  together  in  this  synthesis  sustain  a  de- 
termined and  peculiar  relation  to  one  another. 
If  the  Concepts  be  formed  from  the  subjects  of 
the  Judgments,  those  Judgments  must  have  a 
common — the  same  predicate  ;  if  from  the  pred- 
icates, the  Judgments  must  have  the  same  sub- 
ject. Concepts  are  thus  from  their  very  nature 
relative  cognitions,  and  the  principle  of  relation 
is  in  the  sameness  of  the  term  of  the  Judgment 
which  is  not  synthesized  into  the  Concept — in 
its  Base. 

1  '  Concepts,  however,  differ  from  Judgments, 
as  relative  cognitions,  in  this  respect  :  that  in 
the  Judgment  the  relation  is  explicit,  while  in 
the  Concept  it  is  only  implied.  Thus  in  the 
Judgment,  Man  is  a  rational  animal,  the  rela- 
tion is  articulately  declared  ;  but  in  the  Concept, 


OF  THE   MIND.  199 

Man,  the  relation  to  the  other  term  of  the  Judg- 
ment from  which  it  is  derived,  although  real,  is 
not  expressed,  but  only  implied.  The  Base  of 
the  Concept,  although  real,  is  not  expressed. 

u  Still  further,  a  Concept  is  essentially  a  one- 
sided cognition.  It  is  formed  from  but  one  side 
of  a  Judgment,  from  the  Subject  or  from  the 
Predicate.  It  may  be  regarded,  indeed,  as  an 
aggregate  of  Judgments,  that  is,  a  synthesized 
or  composite  Judgment,  with  the  single  term — 
the  Base,  and  the  Copula  dropped. 

"  A  Concept,  however,  always  implies  the 
Judgments  from  which  it  is  derived  ;  it  implies- 
the  other  term,  which  has  been  dropped,  but 
which  is  the  indispensable  condition  of  its  being 
formed,  and  is,  therefore,  appropriately  denomi- 
nated the  Base  of  the  Concept  ;  and  also  implies 
that  this  Base  has  been  identified  with  each  of 
the  terms  which  compose  the  Concept. 
It  will  occur  to  the  reflecting  mind,  on  this  ex- 
position of  the  mode  in  which  Concepts  are 
formed,  that  they  are  mere  products  of  Thought, 
aggregates  of  Subjects,  or  aggregates  of  Predi- 
cates, and  do  not  imply  necessarily  any  exactly 
corresponding  aggregates  in  the  reality  of  things. 
How  many  individual  subjects  of  Judgments 
shall  be  combined,  or  how  many  predicates,  are 
questions  that  will  be  determined  by  such  con- 
siderations as  those  of  extent  of  observation,, 
practicability  of  aggregation,  convenience  of  use, 
the  needs  of  occasion,  and  the  like.  The  ex- 
tent of  the  aggregation,  therefore,  varies  indefi- 
nitely with  the  occasions  of  Thought  ;  and  it  is. 


£00          Ol$  THE   KNOWING    FACULTIES 

not  to  be  supposed  that  the  constitution  of  things 
around  us  fluctuates  precisely  with  the  fluctua- 
tions of  Thought.  As  the  mathematical  analyst, 
in  the  progress  of  his  demonstration,  finds  it  con- 
venient to  substitute  single  letters  or  symbols  to 
denote  a  number  of  quantities  in  some  respect 
of  like  character,  so  Thought,  for  its  own  mani- 
fold conveniences,  often  aggregates  like  elements 
and  signalizes  them  by  single  words. "  (Day, 
Elements  of  Logic ,  ed.  1868,  pp.  62-66.) 

185.  "  The  Third  gradation  of  Thought  is 
the  Reasoning*  Like  the  Concept,  it  is  de- 
rived from  the  Judgment.  It  differs  from  the 
Concept  in  its  form,  as,  unlike  that,  it  retains  the 
full  forms  of  the  Judgment,  and  accordingly,  also, 
to  a  certain  extent,  it  differs  from  it  in  the  mode 
of  its  derivation.  It  differs  from  the  Judgment 
proper  in  this  respect,  that  it  is  a  derivation 
from  a  Judgment — a  traced  movement  of 
Thought,  supperadded  to  that  which  constitutes 
the  Judgment.  It  is  not  the  derived  Judgment, 
.not  the  mere  terminus,  the  point  at  the  end  of 
the  line  over  which  the  Thought  has  moved,  but 
the  line  itself  as  traced  in  the  movement  of  the 
Thought.  When  viewed  as  a  resultant  product 
of  Thought,  therefore,  it  must  be  regarded  as 
the  track  of  Thought  left  marked  by  the  move- 
ment, not  the  mere  attained  object  or  goal  of  the 
movement,  which  is  nothing  more  than  a  Judg- 
ment. We  are  carefully  to  distinguish,  there- 
fore, a  Reasoning  from  the  Conclusion — from  the 
Judgment  which  is  attained  by  the  reasoning. 

.* '  A  Reasoning,  thus,  is  a  derivation  of  a  Judg- 


OF  THE   MIND.  201 

ment  from  another  Judgment  or  Judgments. 
1  Reasoning  is  a  modification  from  the 
French  raisonner  (and  this  is  a  derivation  from 
the  Latin  ratio),  and  corresponds  to  ratiociatio, 
which  has  indeed  been  immediately  transferred 
into  our  language  under  the  form  of  ratiocina- 
tion. Ratiocination  denotes  properly  the  pro- 
cess, but  improperly,  also,  the  product  of  reason- 
ing ;  Ratiocinium  marks  exclusively  the  product. 
The  original  meaning  of  ratio  was  computa- 
tion, and  from  the  calculation  of  numbers  it  was 
transferred  to  the  process  of  mediate  comparison 
in  general.  Discourse  (discursus,  diavoia)  in- 
dicates the  operation  of  comparison,  the  running 
backward  and  forward  between  the  characters  or 
notes  of  objects  (discurrere  inter  notas,  diavo- 
€10 dai).  The  terms  discourse  and  discursus, 
dictvoia,  are,  however,  often  used  for  the  reason- 
ing process,  strictly  considered,  and  discursive  is 
even  applied  to  denote  mediate,  in  opposition  to 
intuitive,  judgment,  as  is  done  by  Milton.  The 
compound  term,  discourse  of  reason,  unambig- 
uously marks  its  employment  in  this  sense.  Ar- 
gumentation is  derived  from  argumentari, 
which  means  argumentis  uti ;  argument  again, 
argumentum — what  is  assumed  in  order  to  argue 
something — is  properly  the  middle  notion  in  a 
reasoning — that  through  which  the  conclusion  is 
established  ;  and  by  the  Latin  Rhetoricians  it 
was  defined,  *  probabile  invention  ad  faciendam- 
fidem. '  It  is  often,  however,  applied  as  co-exten- 
sive with  argumentation.  Inference  or  Illation 
(from  infero)  indicates  the  carrying  out  into  the 


202          ON   THE   KNOWING   FACULTIES 

last  proposition  what  was  virtually  contained  in 
the  antecedent  judgments.  To  conclude  (con- 
cludere),  again,  signifies  the  act  of  connecting 
and  shutting  into  the  last  proposition  the  two 
notions  which  stood  apart  in  the  two  first.  A 
conclusion  (conclusio)  is  usually  taken,  in  its 
strict  or  proper  signification,  to  mean  the  last 
proposition  of  a  reasoning  ;  it  is,  sometimes, 
however,  used  to  express  the  product  of  the 
whole  process.  To  syllogize  means  to  form  syl- 
logisms. Syllogism  (avJtA&yiffjAOS)  seems  origi- 
nally, like  ratio,  to  have  denoted  a  computa- 
tion— an  adding  up  ;  and  like  the  greater  part 
of  the  technical  terms  of  Logic  in  general,  was 
brorrowed  by  Aristotle  from  the  mathematicians. 
2vXXoyiGjAOS  may,  however,  be  considered 
as  expressing  only  what  the  composition  of  the 
word  denotes — a  collecting  together  ;  for  av\- 
Xoyi^sffdai  comes  from  avKX-eyeiv,,  which 
signifies  to  collect.  Finally,  in  Latin,  a  syllog- 
ism is  called  collectio,  and  to  reason,  colligere. 
This  refers  to  the  act  of  collecting,  in  the  conclu- 
sion, the  two  notions  scattered  in  the  premises./ 
"  A  Reasoning  is  composed  of  two  parts — the 
original  Judgment  or  Judgments  which  are  the 
original  datum  in  the  process,  and  the  move- 
ment of  the  Thought  in  the  process.  As  the 
datum  is  regarded  as  logically  determining  and 
preceding,  it  is  called  the  Antecedent,  and  the 
other  part,  regarded  as  logically  determined,  or 
following,  is  called  the  Consequent.  Its  proper 
sign  is  therefore.  These  are  the  parts  of  a 
Reasoning  regarded  as  an  Integrate  Whole. 


OF  THE   MIND.  203 

u  The  antecedent  in  a  Reasoning  may  consist 
of  a  single  Judgment,  or  of  a  plurality  of  Judg- 
ments. If  it  consist  of  but  one  Judgment,  the 
Reasoning  is  called  an  Immediate  Reasoning  ; 
as,  Man  is  a  rational  animal ;  therefore,  Man  is 
rational.  If  the  antecedent  consists  of  more 
than  one  Judgment,  the  Reasoning  is  called  a 
Mediate  Reasoning,  or,  more  technically,  a  Syl- 
logism." (Day,  "Elements  of  Logic, ' '  ed.  1 868, 
pp.  91-94.) 

186.  "  Reason,  on  the  other  hand,  has  no 
relation  to  the  body,  except  as  the  soul's  lodging 
and  instrument  ;  it  belongs  to  the  soul,  purely 
and   abidingly,   and  may  be  exercised  without 
giving  the  slightest  external  token.     Instead  of 
framing  bodily  organs,     ...     it  spans  the 
sciences,  sails  deliciously  through  the  heavenly 
realms  of  poetic  analogy,  penetrates  the  signifi- 
cance of  things,  and  looks  into  the  very  mind  of 
God  himself. ' '    (Grindon,  Life,  p.  365,  third  ed. , 
London.) 

187.  "  Thinking,  as  Plato  has  observed,  is 
but  the  conversation  of  the  soul  with  herself  ; 
and  the  instrument  employed  is  the  echo  of  that 
which  forms  the  medium  of  communication  with 
others.     To  this  it  may  be  added  that  the  no- 
tion, as  represented  in  language,  is  but  the  sub- 
stitute for  the  notion  embodied  in  intuition,  and 
derives  all  the  conditions  of  its  validity  from  the 
possibility  of  the  latter  ;    for  language,  though 
indispensable  as  an  instrument  of  thought,  lends 
itself  with  equal  facility  to  every  combination, 
and  thus  furnishes  no  criterion  by  which  we  can 


204  ON  THE   NATURE   OF 

judge  between  sense  and  nonsense — between  the 
conceivable  and  the  inconceivable. "  (Mansel, 
Metaphysics,  pp.  1671-68,  ed.  1871.) 

(B)    ON    THE    NATURE    OF    SUBJECT-MATTER. 

-188.  In  addition  to  a  knowledge  of  mind 
and  of  knowing,  the  teacher,  engaged  in  the 
discovery  of  Methods  of  Teaching,  must  dili- 
gently investigate  the  nature  of  the  subject-mat- 
ter that  he  is  to  teach. 

189.  By  nature  of  subject-matter  is  meant 
that  subtle,  original,  and  permanent  property  of 
the  subject-matter,  at  the  presence  of  which  the 
faculties  of  the  mind  are  intuitively  incited  to 
their  specific  activities. 

190.  Some  of  this  matter  lies  in  the  world 
that  is  external  to  the  mind  of   man,    and   is 
called  material. 

191.  Other  matter   rests  exclusively   within 
the  ego.      The  mind  creates  it  both  as  to  its 
matter  and  form.     In  the  case  of  material  sub- 
ject-matter, the  mind  determines  only  the  form 
under  which  it  exists  as   knowledge.      In  the 
other  case,  the  immaterial,  the  matter  and  form 
would  never  exist  as  knowledge,  or  as  matter  for 
knowledge,  were  it  not  for  the  mind.     The  in- 
vestigation of  this  whole  subject  is  too  vast  to 
attempt  to   do  more,  at  this  time,  than  touch 
upon  two  or  three  subjects,  except  in  the  most 
cursory  manner.    The  inquiry  is  directed  towards 
the  nature  of  Object  Teaching,  a  familiar  ex- 
pression, and  the  nature  of  the  subject-matter  of 


SUBJECT-MATTER.  205 

mathematics,  one  branch  of  which,  arithmetic, 
forms  so  important  an  element  in  the  lower 
schools. 

192.  Object  Teaching   is  that  teaching  in 
which  a  knowledge  of  objects,  or  object-matter, 
— or  where  the  subject-matters   are  objects — is 
the  real  end  and  purpose  of  the  instruction.     Ob- 
ject Teaching  regards  a  knowledge  of  objects  as 
an  end — it  does  not  consider  anything  beyond 
the  objects  themselves — it  is  served  fully  when 
this  knowledge  of  facts  is  secured — its  province 
is  with  the  actual,  which  exists  as  individual  facts 
— its  subject-matter  is  that  which  addresses  itself 
exclusively  to  the  perceptive  and  discriminative 
faculties  of  the  mind,  as  matter  to  be  learned 
for  its  own  sake.     The  powers  of  the  mind  that 
are  mainly  instrumental  in  acquisitions  by  the 
learner,  who  is  taught  by  Object  Teaching,  are 
the   perceptive,    which  cognize  intuitively  and 
immediately  ;  the  discriminative,  which  outline 
one  object  from  another  ;  and  memory,  which 
retains.    Whatever  is  purely  distinctive  of  Object 
Teaching  is  found  within  the  above  limitations. 
It  relates  to  the  region  of  individual  facts. 

193.  Wherever    an   abundance    of    facts    is 
wanted  as  materials  for  the  other  faculties  of  the 
mind  to  use  subsequently  in  constructing  science, 
Object  Teaching  is  the  way  by  which  the  ne- 
cessities can  be  met. 

194.  But  Object  Teaching  is  only  possible 
where  a  knowledge  of  facts,  as  such,  is  to  be 
obtained,  and  where  the  materials,  the  matters, 


206  ON   THE   NATURE   OF 

of  knowledge,  exist  as  objects  of  perception  and 
discrimination. 

195.  All  those  ways  of  teaching  where  ob- 
jects, as  charts,   maps,   apparatus,   pictures,    are 
used,  by  the  teacher  and  pupil,  not  as  ends  of 
knowledge  unto    themselves,    but  as  helps,    by 
analogy,  to  acquiring  knowledge  of  other  things 
as  ends — all  these  ways  of  teaching  are  not  Ob- 
jective, they  are  Illustrative. 

196.  Ideas  in  the  memory  are  joined  together 
by  the  nexus  of  their  nature,  termed  the  Laws  of 
Association.     When,  by  any  chance,  one  idea  is 
brought  into  consciousness  from  unconsciousness 
— one  modification  reproduced — the  whole  group 
of  ideas,  related  by  sameness  of  time,  space,  or 
circumstances,  come   flitting   as   flocks   through 
consciousness.     Connected  with  this  association 
of  ideas  is  the   power   of   imagination,    which 
creates  new   mental    beings,    and   which  .seizes 
upon  analogies.     These  states  or  modes  of  the 
activities  make  Illustrative  Teaching  possible. 

197.  Illustrations  are  lights  set  by  the  way- 
side in  parabolic  mirrors,  to  illuminate  obscure 
passages — they  are  voices  which  call  out  a  wel- 
come to  him  who  is  bewildered  in  the  midst  of 
a  mazy    mass   of   half -obscured   and    obscuring 
numbers — they  are  guides  that  accompany  the 
student  to  reveal  to  him  on  a  sudden  the  secret 
labyrinths  through  which  he  may  arise  into  the 
upper  levels  of  light — they  are  the  Aladdin  Lamp 
and   Ring,  by  whose  mystic   power  their   pos- 
sessor may  be  instantaneously  transported  into 


SUBJECT-MATTER.  207 

the  palaces  of  the  Beautiful  and  the  True.  The 
value  of  an  illustration  consists  in  its  brevity, 
its  brilliancy,  its  pointedness,  its  unexpected  and 
unforeseen  applicability,  and  its  convincing  force 
of  plain  analogy. 

4  '  Illustration  is  vivid  elucidation  (  =  to  make 
more  fully  intelligible)  by  certain  specific  and 
effective  means,  as  similitudes,  comparisons,  ap- 
propriate incidents  or  anecdotes,  and  the  like, 
graphic  representations,  and  even  artistic  draw- 
ings. "  (Smith,  Syn.  Discr.) 

"  Analogy  is  often  used  familiarly,  as  if  it 
meant  mere  moral  resemblance  or  similarity. 
Strictly  speaking,  however,  analogy  implies  a 
third  term,  or  four  terms,  as  follows  : — As  A  is 
to  B,  so  is  C  ;  or  as  A  is  to  B,  so  is  C  to  D. 
Analogy,  therefore,  is  similarity  of  relations. 
When  we  argue  from  example,  we  argue  from 
the  likeness  of  things  ;  when  from  analogy,  we 
argue  from  the  likeness  of  their  relations.  If  I 
argue  that,  because  the  seed  dies  in  the  earth 
before  it  springs  up  anew,  therefore  it  is  prob- 
able that  the  human  body  will  rise  again  after 
death  ;  this  is,  as  to  the  character  of  the  idea, 
a  resemblance,  as  to  the  argument,  an  analogy  ; 
the  principle  being  that,  as  the  same  God  is  the 
author  of  a  natural  and  a  spiritual  world,  He 
may  be  expected  to  act  toward  each  upon  similar 
and  common  laws. ' '  (Ibid.) 

"Analogy  and  Induction. — There  are  two 
requisites  in  order  to  every  analogical  argument  : 
1 .  That  the  two  or  several  particulars  concerned 
in  the  argument  should  be  known  to  agree  in 


208  ON  THE   MATURE   OF 

some  one  point  ;  for  otherwise  they  could  not  be 
referable  to  any  one  class,  and  there  would  con- 
sequently be  no  basis  to  the  subsequent  inference 
drawn  in  the  conclusion.  2.  That  the  conclusion 
must  be  modified  by  a  reference  to  the  circum- 
stances of  the  particular  to  which  we  argue. 
For  herein  consists  the  essential  distinction  be- 
tween an  analogical  and  an  inductive  argu- 
ment." (Fleming,  Vocab  Phil.} 

198.  "I  hate  set  dissertations  ;  and,  above 
all  things  in  the  world,  'tis  one  of  the  silliest 
things  in  one  of  them,  to  darken  your  hypothesis 
by  placing  a  number  of  tall,  opake  words,  one 
before  another,  in  a  right  line,  betwixt  your 
own  and  your  reader's  conception, — when,  in  all 
likelihood,  if  you  had  looked  about,  you  might 
have  seen  something  standing,  or  hanging  up, 
which  would  have  cleared  the  point  at  once  ; — 
'  for  what  hindrance,  hurt,  or  harm  doth  the 
laudable  desire  of  knowledge  bring  to  any  man, 
if  even  from  a  sot,  a  pot,  a  fool,  a  stool,  a  win- 
ter-mitten, a  truckle  for  a  pulley,  the  lid  of  a 
goldsmith's  crucible,  an  -oil-bottle,  an  old  slipper, 
or  a  cane-chair  ?'  I  am  this  moment  sitting 
upon  one.  Will  you  give  me  leave  to  illustrate 
this  affair  of  wit  and  judgment,  by  the  two 
knobs  on  the  top  of  the  back  of  it  ? — they  are 
fastened  on,  you  see,  with  two  pegs  stuck  slightly 
into  two  gimlet-holes,  and  will  place  what  I  have 
to  say  in  so  clear  a  light,  as  to  let  you  see  through 
the  drift  and  meaning  of  my  whole  preface,  as 
plainly  as  if  every  point  and  particle  of  it  was 
made  up  of  sunbeams.  I  enter  now  directly 


SUBJECT-MATTER.  209 

upon  the  point.  Here  stands  wit, — and  there 
stands  judgment,  close  beside  it,  just  like  the 
two  knobs  I'm  speaking  of,  upon  the  back  of 
this  self -same  chair  on  which  I  am  sitting.  You 
see,  they  are  the  highest  and  most  ornamental 
parts  of  its  frame, — as  wit  and  judgment  are  of 
ours, — and,  like  them  too,  indubitably  both  made 
and  fitted  to  go  together,  in  order,  as  we  may  say 
in  all  such  cases  of  duplicated  embellishment, 
to  answer  one  another.  Now,  for  the  sake  of 
an  experiment,  and  for  the  clearer  illustrating 
this  matter, — let  us  fora  moment  take  off  one  of 
these  two  curious  ornaments  (I  care  not  which) 
from  the  point  or  pinnacle  of  the  chair  it  now 
stands  on  ; — nay,  don't  laugh  at  it, — but  did 
you  ever  see,  in  the  whole  course  of  your  lives, 
such  a  ridiculous  business  as  this  has  made  of  it  ? 
— Why,  'tis  as  miserable  a  sight  as  a  sow  with  one 
ear  ;  and  there  is  just  as  much  sense  and  sym- 
metry in  the  one  as  in  the  other. — Do, — pray,  get 
off  your  seats,  only  to  take  a  view  of  it. — Now, 
would  any  man  who  valued  his  character  a  straw, 
have  turned  a  piece  of  work  out  of  his  hand  in  such 
a  condition  ? — Nay,  lay  your  hands  upon  your 
hearts,  and  answer  this  plain  question,  Whether 
this  one  single  knob,  which  now  stands  here  like 
a  block-head  by  itself,  can  serve  any  purpose 
upon  earth,  but  to  put  one  in  mind  of  the  want 
of  the  other  ? — and  let  me  farther  ask,  in  case 
the  chair  was  your  own,  if  you  would  not  in 
your  consciences  think,  rather  than  be  as  it  is, 
that  it  would  be  ten  times  better  without  any 
knobs  at  all  ? 


210  ON  THE   STATURE   OF 

"  Now  these  two  knobs,  or  top-ornaments  of 
the  mind  of  man,  which  crown  the  whole  entab- 
lature,— being,  as  I  said,  wit  and  judgment, 
which,  of  all  others,  as  I  have  proved  it,  are  the 
most  needful,  — the  most  prized, — the  most  cal- 
amitous to  be  without,  and  consequently  the  hard- 
est to  come  at  ; — for  all  these  reasons  put  togeth- 
er, there  is  not  a  mortal  among  us  so  destitute  of  a 
love  of  good  fame  or  feeding, — or  so  ignorant  of 
what  will  do  him  good  therein, — who  does  not 
wish  and  steadfastly  resolve  in  his  own  mind,  to 
be,  or  to  be  thought  at  least,  master  of  the  one 
or  the  other,  and  indeed  of  both  of  them,  if  the 
thing  seems  any  way  feasible,  or  likely  to  be 
brought  to  pass. ' '  (Sterne,  Tristram  Shandy,  pp. 
88-9,  ed.  1844,  Philadelphia.) 

199.  Illustrative  Teaching  is  seeking  some- 
thing that  bears  a  resemblance  in  form,  nature, 
or  kind  to  the  point  to  be  learned,  or  taught, 
presenting  it  instead  of  the  point,  and  thus  en- 
abling the  powers  of  comparison  possessed  by 
the  pupil  to  act  by  inference  from  the  analogy. 
This  is  a  process  of  extending  the  meaning  of 
words,  called  sometimes  "  the  process  of  analo- 
gous or  metaphorical  extension  of  the  meaning 
of  words.  This  change  may  be  said,  no  doubt, 
to  consist  in  generalization,  since  there  must 
always  be  a  resemblance  between  the  new  and 
old  applications  of  the  term.  But  the  resem- 
blance is  often  one  of  a  most  distant  and  obscure 
kind,  such  as  we  should  call  analogy  rather  than 
identity. "  (Jevons,  El.  Lessons  in  Logic,  p.  50, 
ed.  1878.) 


SUBJECT-MATTER.  211 

200.  Example  would  be  something  akin  to 
analogy,  excepting  that  example  may  be  of  the 
kind  of  thing  itself,  as  well  as  ah  example  illus- 
trating the  case  at  issue. 

201.  Illustrative  Teaching  is    often    called, 
unfortunately  in  conception,  Objective  Teaching. 
An  object  can  be  used  for  but  two  possible  pur- 
poses  in  teaching  :  (1)  To  be  learned,   in  and 
for  itself  ;  (2)  Or  to  be  an  aid  in  learning  some- 
thing else.     The  first  is  Object  Teaching,  the 
second  is  Illustrative  Teaching. 

202.  The  distinction  between  the   province 
of    Object   Teaching   and   that    of    Illustrative 
Teaching  has  been  indistinctly  apprehended  by 
teachers.     This  misapprehension  has  led  to  se- 
rious obscurity  of  conceptions  of  teaching,   for 
the    expression   Object  Teaching   has  been  ap- 
plied without  discrimination  to  all  kinds  of  teach- 
ing where  objects  were  used,  whatever  their  pur- 
pose, whether  as  objects  to  be  learned,  or  as  ob- 
jects to  use  in  illustrating  other  points. 

' 1  The  science  which  enlightens,  and  the  phys- 
ick  that  cures,  are  doubtless  very  useful  :  but 
the  pretended  science  that  misleads,  and  the 
physick  that  kills,  are  as  certainly  destructive. 
Teach  us,  therefore,  to  distinguish  between  them. 
.  .  It  may  be  replied,  as  it  constantly  is, 
the  fault  is  in  the  physician,  and  not  in  the  sci- 
ence of  medicine,  which  is  otherwise  infallible. 
Well,  well,  be  it  so  :  take  care,  however,  the 
physick  be  never  accompanied  by  the  doctor  : 
for,  as  sure  as  ever  they  come  together,  there 
will  be  an  hundred  times  more  to  fear  from  the 


212  ON  THE   NATURE   OF 

blunders  of  the  artist,  than  to  hope  for  from  the 
efficacy  of  the  art."  (Rousseau,  JEmilius,  Vol. 
L,  pp.  45-6.) 

203.  It  has  already  been  remarked  that  Ob- 
ject Teaching  can  be  resorted  to  only  with  those 
subjects  where  facts  obtained  by  perception  and 
discrimination  are  desired.  There  are  branches 
to  be  taught  where  it  is  impossible,  from  the 
nature  of  the  subject-matter,  to  teach  in  this 
way.  The  subject  of  mathematics  is  one  that 
has  grown  from  a  basis  of  definitions.  The  axi- 
oms follow  definitions,  but  they  are  phases  of 
conclusive  reasoning,  and  assume  things  which 
are  the  creations  of  definitions.  Definitions  are 
the  bases  of  mathematic  science  in  its  matter. 
Axioms  are  the  bases  in  its  logical  processes  of 
reasoning.  Definitions  are  things  which  are  prod- 
ucts growing  out  of  relations.  Relations  are  ob- 
jects only  as  they  are  products  of  the  activities  of 
the  faculty  of  Thought.  Hence  all  mathematical 
subjects  are,  from  their  nature,  incapable  of  be- 
ing taught  objectively.  All  lines,  mathematical 
blocks,  charts,  astronomical  apparatus,  and  cal- 
culating machines,  are  but  objects  which  illus- 
trate mathematical  truths,  its  definitions,  and 
results,  as  intellectual  products — they  are  not  the 
things  which  are  learned  in  themselves.  What 
are  called  Applied  Mathematics  are  only  hypo- 
thetical illustrations  of  mental  creations.  It  is 
also  true  that  this  science  is  one  ' '  in  whose  reas- 
onings both  matter  and  form  can  be  furnished 
by  the  mind  itself,"  and  not  one  where  "  the 
form  alone  is  from  the  mind,  the  matter  being 


SUBJECT-MATTER. 

derived  from  experience."    (Manse],  Prol.  Log* 
p.  93,  ed.  1860.) 

204.  "  Abstract  terms  are  strongly  distin- 
guished from  general  terms  by  possessing  only 
one  kind  of  meaning  ;  for  as  they  denote  quali- 
ties there  is  nothing  which  they  cannot  in  addi- 
tion imply.  The  adjective  '  red '  is  the  name 
of  red  objects,  but  it  implies  the  possession  by 
them  of  the  quality  redness ;  but  this  latter 
term  has  one  single  meaning — the  quality  alone. 
Thus  it  arises  that  abstract  terms  are  incapable 
of  plurality."  (Jevons,  Prin.  Science,  p.  27,  ed. 
1877.).  .  .  "  Numerical  Abstraction  consists  in 
abstracting  the  character  of  the  difference  from 
which  plurality  arises,  retaining  merely  the  fact. 
When  I  speak  of  three  men  I  need  not  at  once 
specify  the  marks  by  which  each  may  be  known 
from  each.  Those  marks  must  exist  if  they  are 
really  three  men  and  not  one  and  the  same,  and 
in  speaking  of  them  as  many  I  imply  the  exist- 
ence of  the  requisite  differences.  Abstract 
number,  then,  is  the  empty  form  of  difference  ; 
the  abstract  number  three  asserts  the  existence 
of  marks  without  specifying  their  kind.  Num- 
erical abstraction  is  thus  seen  to  be  a  different 
process  from  logical  abstraction,  for  in  the  latter 
process  we  drop  out  of  notice  the  very  existence 
of  difference  and  plurality.  .  .  .  The  ori- 
gin of  the  great  generality  of  number  is  now  ap- 
parent. Three  sounds  differ  from  three  colours, 
or  three  riders  from  three  horses  ;  but  they  agree 
in  respect  of  the  variety  of  marks  by  which  they 
can  be  discriminated.  The  symbols  1  -f- 1  -f- 1  are 


ON   THE   NATURE   OF 

thus  the  empty  marks  asserting  the  existence  of 
discrimination.  But  in  dropping  out  of  sight 
the  character  of  the  differences  we  give  rise  to 
new  agreements  on  which  mathematical  reason- 
ing is  founded.  .  .  .  The  common  distinc- 
tion between  concrete  and  abstract  number  can 
now  be  easily  stated.  In  proportion  as  we  speci- 
fy the  logical  characters  of  the  things  numbered, 
we  render  them  concrete.  In  the  abstract  num- 
ber three  there  is  no  statement  of  the  points  in 
which  the  three  objects  agree  ;  but  in  three  coins, 
three  men,  or  three  horses,  not  only  are  the  ob- 
jects numbered,  but  their  nature  is  restricted. 
Concrete  number  thus  implies  the  same  con- 
sciousness of  difference  as  abstract  number,  but 
it  is  mingled  with  a  groundwork  of  similarity 
expressed  in  the  logical  terms.  There  is  identity 
so  far  as  logical  terms  enter  ;  difference  so  far  as 
the  terms  are  merely  numerical.  The  reason 
of  the  important  Law  of  Homogeneity  will  now 
be  apparent.  This  law  asserts  that  in  every 
arithmetical  calculation  the  logical  nature  of  the 
things  numbered  must  remain  unaltered.  The 
specified  logical  agreement  of  the  things  must 
not  be  affected  by  the  unspecified  numerical 
differences.  A  calculation  would  be  palpably 
absurd  which,  after  commencing  with  length, 
gave  a  result  in  hours.  It  is  equally  absurd,  in 
a  purely  arithmetical  point  of  view,  to  deduce 
areas  from  the  calculation  of  lengths,  masses 
from  the  combination  of  volume  and  density,  or 
momenta  from  mass  and  velocity.  It  must  re- 
main for  subsequent  consideration  to  decide  in 


SUBJECT-MATTER.  215 

what  sense  one  may  truly  say  that  two  linear 
feet  multiplied  by  two  linear  feet  give  four  su- 
perficial feet  ;  arithmetically  it  is  absurd,  be- 
cause there  is  a  change  of  unit.  As  a  general 
rule  we  treat  in  each  calculation  only  objects  of 
one  nature.  We  do  not,  and  cannot  properly 
add,  in  the  same  sum  yards  of  cloth  and  pounds 
of  sugar.  We  cannot  even  conceive  the  result 
of  adding  area  to  velocity,  or  length  to  density, 
or  weight  to  value.  The  units  added  must  have 
a  basis  of  homogeneity,  or  must  be  reducible  to 
some  common  denominator.  Nevertheless  it  is- 
possible,  and  in  fact  common,  to  treat  in  one 
complex  calculation  the  most  heterogeneous  quan- 
tities, on  the  condition  that  each  kind  of  object 
is  kept  distinct,  and  treated  numerically  only  in 
conjunction  with  its  own  kind.  Different  units, 
so  far  as  their  logical  differences  are  specified,  must 
never  be  substituted  one  for  the  other.  (Ibid., 
pp.  158-60.) 

"  Abstractly  considered,  Number  is  the  measure 
of  the  relation  between  quantities  or  things  of  the 
same  kind.  We  can  form*  no  conception  of  the 
absolute  magnitude  of  any  quantity,  and  can  only 
acquire  a  relative  conception  of  it,  by  comparing 
it  with  some  other  quantity  of  the  same  kind, 
assumed  as  a  standard  of  comparison.  The 
comparison  is  made  by  seeking  how  many  times 
the  standard  is  contained  in  the  quantity  mea- 
sured. The  result  of  this  comparison  is  a 
number."  (Davies  and  Peck,  Diet,  of  Math.) 

"  Groups  of  units  are  what  we  really  treat  in 
arithmetic.  The  number  five  is  really  1  + 1  -f  1 


216  ON  THE   NATURE   OF 

+ 1  + 1 ,  but  for  the  sake  of  conciseness  we  sub- 
stitute the  more  compact  sign  5,  or  the  name 
five.  These  names  being  arbitrarily  imposed  in 
any  one  manner,  an  infinite  variety  of  relations 
spring  up  between  them  which  are  not  in  the 
least  arbitrary.  If  we  define  four  as  1  +  1  +  1  +  1, 
and  five  as  1  +  1  +  1  +  1  +  1,  then  of  course  it 
follows  that  five=four  +  l  ;  but  it  would  be 
•equally  possible  to  take  this  latter  equality  as  a 
definition,  in  which  case  one  of  the  former  equali- 
ties would  become  an  inference.  It  is  hardly  re- 
quisite to  decide  how  we  define  the  names  of 
numbers,  provided  we  remember  that  out  of  the 
infinitely  numerous  relations  of  one  number  to 
others,  some  one  relation  expressed  in  an  equali- 
ty must  be  a  definition  of  the  number  in  question 
and  the  other  relations  immediately  become  nec- 
essary inferences. 

"  In  the  science  of  number  the  variety  of 
classes  which  can  be  formed  is  altogether  infinite, 
and  statements  of  perfect  generality  may  be 
made  subject  only  to  difficulty  or  exception  at 
the  lower  end  of  the  scale.  Every  existing 
number  for  instance  belongs  to  the  class  M  +  7  ; 
that  is,  every  number  must  be  the  sum  of  another 
number  and  seven,  except  of  course  the  first  six 
or  seven  numbers,  negative  quantities  not  being 
here  taken  into  account.  Every  number  is  the 
half  of  some  other,  and  so  on.  The  subject  of 
generalization,  as  exhibited  in  mathematical 
truths,  is  an  infinitely  wide  one.  In  number 
we  are  only  at  the  first  step  of  an  extensive  series 
of  generalizations.  As  number  is  general  com- 


SUBJECT-MATTER.  217 

pared  with  the  particular  things  numbered,  so 
we  have  general  symbols  for  numbers,  and  gen- 
eral symbols  for  relations  between  undetermined 
numbers.  There  is  an  unlimited  hierarchy  of 
successive  generalizations. "  (Jevons,  Pr.  Sc., 
pp.  167-168.) 

"  A  large  proportion  of  the  mathematical 
functions  which  are  conceivable  have  no  applica- 
tion to  the  circumstances  of  this  world.  Phy- 
sicists certainly  do  investigate  the  nature  and 
consequences  of  forces  which  nowhere  exist. 
Newton's  Principia  is  full  of  such  investigations. 
In  one  chapter  of  his  Mecanique,  Celeste  Laplace 
indulges  in  a  remarkable  speculation  as  to  what 
the  laws  of  motion  would  have  been  if  momen- 
tum, instead  of  varying  simply  as  the  velocity, 
had  been  a  more  complicated  function  of  it. 
.  Thought  is  not  bound  down  to  the  limits 
of  what  is  materially  existent,  but  is  circum- 
scribed only  by  those  Fundamental  Laws  of 
Identity,  Contradiction,  and  Duality,  which  have 
'already  been  laid  down,"  (Ibid.,  pp.  70-45.) 

205.  "  Mathematical  Judgments  may  be  di- 
vided into  two  kinds — indemonstrable  or  axiom- 
atic judgments,  whose  necessity  is  self-evident  ; 
and  demonstrable  judgments,  whose  necessity 
depends  on  some  previous  assumption.  The 
necessity  of  the  latter  is  derived  from  that  of  the 
former,  so  that  the  indemonstrable  judgments 
alone  require  a  special  examination.  Under 
this  class  are  comprehended  the  axioms  of  geom- 
etry, properly  so-called — viz.,  the  original  as- 
sumptions concerning  magnitudes  in  space  as 


218  ON   THE    NATURE    OF 

such,  and  the  propositions  belonging  to  the  fun- 
damental operations  of  arithmetic — addition  and 
subtraction.  (Distinguish  between  postulates,  and 
some  axioms  which  are  logical,  not  geometrical 
principles,  and  depend  solely  on  the  laws  of 
thought.)  (Though  in  some  things,  as  in  num- 
bers, besides  adding  and  subtracting,  men  name 
other  operations,  as  multiplying  and  dividing, 
yet  are  they  the  same  ;  for  multiplication  is  but 
adding  together  of  things  equal  ;  and  division 
but  subtracting  of  one  thing  as  often  as  we  can. 
Hobbes,  Leviathan,  p.  L,  chap.  5.)  The  ne- 
cessity of  these  judgments  results  from  the  exist- 
ence in  the  mind  of  the  a  priori  forms  of  intui- 
tion— Space  and  Time.  The  axioms  of  geometry 
are  self-evident  statements  concerning  magni- 
tudes in  space  ;  such  as  that  two  straight  lines 
cannot  enclose  a  space.  Their  self-evidence  or 
necessity  is  to  be  explained  by  the  circumstance 
that  the  presented  intuition,  as  well  as  the  repre- 
sentative thought,  is  derived  from  within,  not 
from  without.  For  geometrical  propositions  are 
primarily  necessary,  not  as  truths  relating  to  ob- 
jects without  the  mind,  but  as  thoughts  relating 
to  objects  within  :  their  necessity,  as  regards 
real  objects,  is  only  secondary  and  hypothetical. 
If  there  exist  anywhere  in  the  world  two  perfect 
straight  lines,  those  lines  cannot  enclose  a  space  ; 
but  if  such  lines  exist  nowhere  but  in  my  imagi- 
nation, it  is  equally  true  that  I  cannot  think  of 
them  as  invested  with  the  contrary  attributes. 
This  necessity  of  thought  is  dependent  on  a  cor- 
responding necessity  of  intuition.  The  object 


SUBJECT-MATTER.  219 

of  which  pure  geometry  treats  is  not  dependent 
on  sensation,  but  sensation  on  it  :  it  is  a  condi- 
tion under  which  alone  sensible  experience  is 
possible  ;  and  therefore  its  characteristics  must 
accompany  all  our  thoughts  concerning  any  pos- 
sible object  of  such  experience  ;  for,  however 
much  we  may  abstract  from  the  attributes  of 
this  or  that  particular  phenomenon  of  experience, 
we  are  clearly  incompetent  to  deprive  it  of  those 
conditions  under  which  alone,  from  the  consti- 
tution of  our  minds,  experience  itself  is  possible. 
We  can  perceive  only  as  we  are  permitted  by 
the  laws  of  our  perceptive  faculties,  as  we  can 
think  only  in  accordance  with  the  laws  of  the  un- 
derstanding. If,  then,  by  a  law  of  rny  percep- 
tive faculty,  I  am  compelled  to  regard  all  ob- 
jects as  existing  in  space,  the  attributes  which 
are  once  presented  to  me  as  the  properties  of  a 
given  portion  of  space,  such  as  the  pair  of 
straight  lines  now  present  to  my  sight  or  imagi- 
nation, must  necessarily  be  thought  as  existing 
in  all  space  and  at  all  times.  For  to  imagine  a 
portion  of  space  in  which  such  properties  are 
not  found,  would  not  be  to  imagine  merely  a 
different  combination  of  sensible  phenomena, 
such  as  continually  takes  place  without  any  change 
in  the  laws  of  sensibility  :  it  would  be  to  imagine 
myself  as  perceiving  under  other  conditions  than 
those  to  which,  by  a  law  of  my  being,  I  am  sub-  / 
jected.  But  a  condition,  though  potentially  ex- 
isting in  the  original  constitution  of  the  mind, 
is  actually  manifested  only  in  conjunction  with 
that  of  which  it  is  the  condition.  Space,  there- 


220  ON  THE   NATUKE   OF 

fore,  and  its  laws,  are  first  made  known  to  con- 
.  sciousness  on  the  occasion  of  an  actual  phenom- 
enon of  sense.  Hence  the  twofold  character  of 
geometrical  principles  :  empirical,  as  suggested 
in  and  through  an  act  of  experience  ;  necessary, 
as  relating  to  the  conditions  under  which  alone 
such  experience  is  possible  to  human  faculties. 

' '  Arithmetic  is  related  to  Time  as  Geometry 
to  Space  ;  and  the  necessity  of  its  propositions 
may  be  explained  upon  similar  principles.  The 
two  sciences,  however,  present  some  important 
features  of  distinction.  Most  of  the  proposi- 
tions of  geometry  are  deductive  :  it  contains 
very  few  axioms,  properly  so  called,  and  its  pro- 
cesses consist  in  the  demonstration  of  a  multi- 
tude of  dependent  propositions  from  the  combi- 
nation of  these  axioms  with  certain  logical  prin- 
ciples of  thought  in  general.  On  the  other 
hand,  the  fundamental  operations  of  arithmetic 
— addition  and  subtraction — present  to  us  a  vast 
number  of  independent  judgments,  every  one  of 
which  is  derived  immediately  from  intuition, 
and  cannot,  by  any  reasoning  process,  be  de- 
duced from  any  of  the  preceding  ones.  (Although 
it  is  simpler  to  regard  addition  and  subtraction 
as  independent  processes,  yet  no  result  of  either 
can  be  derived  from  a  preceding  result  of  the 
same  operation. )  Pure  geometry  cannot  advance 
a  step  without  demonstration,  and  its  processes 
are  therefore  all  reducible  to  the  syllogistic  form. 
Pure  arithmetic  contains  no  demonstration  ; 
and  it  is  only  when  its  calculus  is  applied  to  the 
solution  of  particular  problems  that  reasoning 


SUBJECT-MATTER.  221 

takes  place,  and  the  laws  of  the  syllogism  be- 
come applicable.  It  is  not  reasoning  which  tells 
us  that  two  and  two  make  four  ;  nor,  when  we 
have  gained  this  proposition,  can  we  in  any  way 
deduce  from  it  that  two  and  four  make  six. 
We  must  have  recourse,  in  each  separate  case, 
to  the  senses  or  the  imagination  (memory),  and 
by  counting  up  the  individual  succession  corre- 
sponding to  each  term,  intuitively  perceive  the 
resulting  sum.  The  intuition  thus  serves  nearly 
the  same  purpose  as  the  figure  in  a  geometrical 
demonstration  ;  with  the  exception  that,  in  the  lat- 
ter case,  the  construction  is  adopted  to  furnish  pre- 
mises to  a  proposed  conclusion  ;  while  in  the  for- 
mer it  gives  us  a  judgment  which  we  have  no  im- 
mediate intention  of  applying  to  any  further  use. 
"  The  intuition  in  the  case  of  arithmetic  is 
furnished  by  the  consciousness  of  successive 
states  of  our  own  minds.  Setting  aside  all  other 
characteristics  of  those  states,  save  that  of  their 
succession  in  time,  we  have  the  immediate  con- 
sciousness of  one,  two,  three,  four,  etc.  A 
purely  natural  arithmetic  would  consist  in  carry- 
ing on  this  series,  with  no  other  relation  between 
its  members  but  that  of  succession,  until  the 
memory  became  unable  to  continue  the  process. 
The  artificial  methods  by  which  calculation  is  fa- 
cilitated and  extended,  such  as  that  of  a  scale  of 
notation,  in  which  the  series  recommences  after 
a  certain  number  of  members,  vastly  increase  the 
utility  of  the  calculus,  but  do  not  affect  its  psy- 
chological basis.  To  construct  the  science  of 
arithmetic  in  all  its  essential  features,  it  is  only 


222  ON   THE   NATURE   OF 

necessary  that  we  should  be  conscious  of  a  suc- 
cession in  time,  and  should  be  able  to  give  names 
to  the  several  members  of  the  series  ;  and  since 
in  every  act  of  consciousness  we  are  subject  to 
the  condition  of  succession,  it  is  impossible  in 
any  form  of  consciousness  to  represent  to  our- 
selves the  facts  of  arithmetic  as  other  than  they 
are. 

"  The  necessity  of  propositions  in  geometry 
and  arithmetic  is  thus  derived  from  their  relation 
to  the  universal  forms  of  intuition — Space  and 
Time.  We  can  suppose  the  possibility  of  be- 
ings existing  whose  consciousness  has  no  relation 
to  space  or  time  at  all.  This  is  no  more  than  to 
admit  the  possible  existence  of  intelligent  beings 
otherwise  constituted  than  ourselves,  and  conse- 
quently incomprehensible  by  us.  But  to  sup- 
pose the  existence  of  geometrical  figures  or  arith- 
metical numbers  such  as  those  with  which  we 
are  now  acquainted,  is  to  suppose  the  existence 
of  space  and  time  as  we  are  now  conscious  of 
them,  and  therefore  relatively  to  beings  whose 
mental  constitution  is  so  far  similar  to  our  own. 
Such  a  supposition  necessarily  carries  with  it  all 
the  mathematical  relations  in  which  space  and 
time,  as  given  to  us,  are  necessarily  thought. 
For  mathematical  judgments  strictly  relate  only 
to  objects  of  thought  as  existing  in  my  mind, 
not  to  distinct  realities  existing  in  relation  to  my 
mind.  They  therefore  imply  no  other  exist- 
ence than  that  of  a  thinking  subject,  modified 
in  a  certain  manner.  Destroy  this  subject,  or 
change  its  modification,  and  we  cannot  say,  as 


SUBJECT-MATTER.  223 

in  other  cases,  that  the  object  may  possibly  exist 
still  without  the  subject,  or  may  exist  in  a  new 
relation  to  a  new  subject  ;  for  the  object  exists 
only  in  and  through  that  particular  modification 
of  the  subject,  and,  on  any  other  supposition,  is 
annihilated  altogether.  Thus  it  is  impossible  to 
suppose  that  a  triangle  can,  in  relation  to  any 
intelligence  whatever,  have  its  angles  greater  or 
less  than  two  right  angles,  or  that  two  and  two 
should  not  be  equal  to  four  ;  though  it  is  quite 
possible  to  suppose  the  existence  of  intelligent 
beings  destitute  of  the  idea  of  a  triangle  or  of 
the  number  two.  This  is  a  necessary  matter 
in  the  strict  sense  of  the  term  ;  a  relation  which 
our  own  minds  are  incapable  of  reversing,  not 
merely'  positively,  in  our  own  acts  of  thought, 
but  also  negatively,  by  supposing  others  who 
can  do  so."  (Mansel,  Metaphysics,  pp.  226-31. 
ed.  1871.) 

206.  "  The  main  branches  of  mathematical 
science  were  formerly  stated  to  be  arithmetic  and 
geometry,  springing  out  of  the  simple  notions 
of  number  and  space.  This  is  too  limited  a  de- 
scription. Unquestionably  the  science  of  num- 
bers, strictly  and  demonstratively  treated,  and 
that  of  geometry,  or  the  deduction  of  the  ele- 
mentary properties  of  figure  from  definitions 
which  are  entirely  exclusive  of  numerical  consid- 
erations, must  be  considered  as  the  elementary 
foundations,  but  not  as  the  ultimate  divisions,  of 
mathematics.  To  them  we  must  add  the  science 
of  operation,  or  algebra  in  its  widest  sense, — the 
method  of  deducing  from  symbols  which  imply 


224:  OX  THE   NATURE   OF 

operations  on  magnitude,  and  which  are  to  be 
used  in  a  given  manner,  the  consequences  of  the 
fundamental  definitions.  The  leading  idea  of 
this  science  is  operation  or  process,  just  as  num- 
ber is  that  of  arithmetic,  and  space  and  figure  of 
geometry  :  it  is  of  a  more  abstract  and  refined 
character  than  the  latter  two,  only  because  it  does 
not  immediately  address  itself  to  the  notions 
which  are  formed  in  the  common  routine  of  life. 
It  is  the  most  exact  of  the  exact  sciences,  accord- 
ing to  the  idea  of  their  exactness  which  frequent- 
ly entertained,  being  more  nearly  based  upon 
definition  than  either  arithmetic  or  geometry. 
It  is  true  that  the  definitions  must  be  such  as  to 
present  results  which  admit  of  application  to 
number,  space,  force,  time,  &c.,  or  the  science 
would  be  useless  in  mathematics,  commonly  so 
called  ;  but  it  is  not  the  less  true  that  a  system 
of  methods  of  operation,  based  upon  general 
definitions,  and  conducted  by  strict  logic,  may 
be  made  to  apply  either  to  arithmetic  or  geome- 
try, according  to  the  manner  in  which  the  gen- 
eralities of  the  definition  are  afterwards  made 
specific.''  (English  Cyclopaedia,  Mathematics.) 
207.  "  The  methods  of  observation  of  quan- 
tity in  general  are,  Numeration,  which  is  pre- 
cise by  the  nature  of  number  ;  the  Measurement 
of  Space  and  Time,  which  are  easily  made  pre- 
cise ;  the  Conversion  of  Space  and  Time,  by 
which  each  aids  the  measurement  of  the  other  ; 
the  Method  of  Repetition  ;  the  Method  of  Coinci- 
dence or  Interferences. ' '  (Whewell,  Nov.  Org. 
Ren.  p.  145.) 


SUBJECT-MATTER.  225 

208.  The  branches  known  as  the  Natural  Sci- 
ences can  be  taught  by  Object  Teaching  in  so 
far  as  facts  are  needed  and  can  be  observed,  for 
the  things  shown  or  observed  are  the  immediate 
objects  to  be  learned.     History  cannot,  from  its 
nature,  be  taught  objectively,  except  it  happen 
that  the  learner  can  be   an   eyewitness  of  the 
events  narrated.     Language  and  Literature  can 
be  taught  by  Object  Teaching,  they  being  ends 
unto   themselves,    and   subjects    of    inspection. 
Applied  mathematics,  being  themselves  illustra- 
tions, can  hardly  be  taught  illustratively. 

209.  As  soon  as  perception  and  determina- 
tion have  given  to  the  mind  knowledge  of  indi- 
vidual facts,  the  power  of  retention  holds  them 
for  future  use — they  are  reproduced  and  repre- 
sented in  consciousness  where    Thought  seizes 
them,  and  constructs  science  from  them.     When 
knowledge  of  individual  objects  is  gained,  the 
usefulness  of  the  objects  ceases.     All  beyond  is 
a  work  of  the  power  of  Thought.      Hence  the 
stages,  for  subject  matter  that  will  admit  of  it, 
are  : — (1)  Knowledge  of  facts  obtained  by  Per- 
ception and  Discrimination,  which  is  the  prov- 
ince of  Object   Teaching  ;  (2)  The    activity  of 
Thought  upon  this  knowledge,  aided  as  it  may 
be  by  Imagination.     In  this  second  stage,  Ob- 
jects are  rather  a  hindrance  if  present  than  an 
aid,  because  they  are  so  much  useless  material 
that  should  be  put  aside — Perception  has  done 
its  work,  Discrimination  has  separated,  and  now 
the  senses  may  slumber  while  Thought  is  rearing 
science  out  of  similarities  and  identities — any 


226  ON   THE   NATURE   OF 

energy  of  attention  which  is  diverted,  at  this 
time,  towards  the  objects  themselves  is  so  much 
abstracted  from  Thought,  which  is  thereby  weak- 
ened, and  Science  so  much  endangered,  for  Sci- 
ence is  not  possible  without  Thought. 

4  i  A  real  experiment  is  a  very  valuable  product 
of  the  mind,  requiring  great  knowledge  to  invent 
it  and  great  ingenuity  to  carry  it  out. 
It  may  be  said  that  a  boy  takes  more  interest  in 
the  matter  by  seeing  for  himself,  or  by  perform- 
ing for  himself,  that  is  by  working  the  handle 
of  the  air-pump  :  this  we  admit,  while  we  con- 
tinue to  doubt  the  educational  value  of  the  trans- 
action. .  .  .  The  function  of  experiment, 
properly  so  called,  in  the  investigation  of  the 
laws  and  processes  of  nature  can  hardly  be  unduly 
exalted  ;  but  it  may  be  said  of  the  experimenter, 
as  of  the  poet,  that  he  is  born  and  not  manufac- 
tured. "  (I.  Todhunter,  Conflict  of  Studies,  pp. 
16-19.) 

210.  Ignorance  of  the  province  of  Object 
Teaching  leads  to  disaster,  in  practice,  in  mental 
discipline.  This  teaching  addresses  the  attention 
of  Perception  and  Discrimination.  Then  the  ob- 
jects have  served  their  purpose.  If  the  knowl- 
edge of  facts  which  the  learner  has  obtained  be 
not  wrought  up  by  Thought  into  Concepts,  which 
are  general  in  their  character  and  form  the  data 
for  Reasoning,  his  mind  is  left  far  short  of  dis- 
cipline. For  true  intellectual  power  comes  only 
by  constant  exercise  of  Thought,  and  Thought 
busies  itself  only  with  mental  products.  Neglect 
of  demanding  maximum  amounts  of  work  for 


SUBJECT-MATTER.  227 

the  powers  of  Thought  of  pupils  habituates  them 
to  superficial  scholarship — they  may  be  apt  at 
observing,  when  objects  are  placed  before  them, 
but  they  will  develop  little  power  of  independent 
research,  of  vigorous  application  to  thinking,  or 
of  the  power  to  generalize.  The  mere  acquisi- 
tion and  memorizing  of  a  number  of  isolated, 
heterogeneous,  or  unrelated  facts,  is  neither  learn- 
ing nor  discipline,  whether  the  facts  are  obtained 
from  personal  observation  and  examination,  from 
oral  statements  of  teachers,  or  gleaned  from 
books. 

(c)    ON    DISCOVERING    METHODS    OF    TEACHING 
SPECIAL    SUBJECTS. 

211.  Having  outlined  the  powers  of  know- 
ing and  the  nature  of  subject-matter,  it  yet  re- 
mains to  investigate  the  Methods  of  Teaching, 
when  they  are  to  be  applied  in  the  teaching  of 
any  given  subject.  "  In  every  Treatise  upon 
any  §cience  two  Points  are  indispensably  re- 
quired ;  the  First,  that  the  science  which  is  the 
subject  of  it  be  fully  explained  ;  the  second, 
.  that  plain  Directions  be  given,  how  and 
by  what  method  such  science  may  be  attained. ' ' 
(Longinus,  On  The  Sublime,  pp.  1—2,  Tr.  by 
Wm.  Smith,  1739,  London.)  It  is  not  the 
purpose  of  this  discussion  to  develop  a  complete 
Method  and  Mode  in  any  subject — simply  to 
present  the  magnitude,  importance,  and  direction 
in  general,  of  Methods  in  special  studies.  To 
discover  a  Method  to  teach  any  branch  is  no 


228         ON   DISCOVERING   METHODS   OF 

easy  task.  The  exact  psychological  faculties  to 
be  addressed  are  often  difficult  to  name — the 
subject-matter  must  be  maintained  in  its  integrity 
while  it  is  manipulated  into  a  system  to  suit  the 
capacities  of  the  mind  taught.  This  latter  point 
is  all  important,  as  it  sometimes  happens  that 
the  truths  of  science  are  sacrificed  to  error  when 
they  appear  in  Modes  of  Teaching.  It  often 
happens  that  systems,  in  their  steps  or  degrees 
of  advancement,  do  only  scant  justice  to  the 
mind  to  be  taught,  because  they  are  too  diffuse, 
too  prolix,  too  narrow  in  their  steps,  or  too  in- 
elastic. These  faults  of  systems  are  grave  ones, 
and  show  the  teacher  uninformed  concerning 
Methods  of  Teaching.  The  subject-matter 
should  be  properly  divided  and  subdivided,  but 
never  below  the  present  attainments  of  the 
learner,  for  mind  grows  from  reaching  out  after 
the  unknown  and  the  difficult,  provided  it  be  not 
clouded  by  discouragement  in  the  pursuit.  The 
subject-matter  should  be  carefully  freed  from  all 
that  is  not  to  be  learned  in  that  lesson — the 
steps  to  be  presented  should  be  those  which  are 
vital  to  the  system  of  the  subject  taught.  Too 
many  words  and  points,  and  too  much  related 
subject-matter,  distract  the  mind  of  the  learner 
so  that  the  real  and  vital  points  are  only  dimly 
apprehended.  He  is  most  fortunate  in  the  class- 
room who  sets  forth,  in  sharp  outline,  just  the 
maximum  of  subject-matter  for  his  class — in- 
spiring a  zeal  and  determination  for  an  increased 
power  on  the  morrow's  lesson. 

212.  Suppose  that  a  teacher  wishes  to  dis- 


TEACHING   SPECIAL  SUBJECTS.          229 

cover  the  Method  of  Teaching  children  the  pro- 
cess of  Adding  Numbers.  How,  in  practice, 
shall  he  proceed  ? 

1.  Concerning  the  nature  of  the  subject-mat- 
ter : 

(a)  Addition,  being  purely  mathematical 
in  its  nature,  is  incapable  of  being 
presented  by  Object  Teaching. 

(£)  Being  capable  of  a  hypothetical  ap- 
plication to  material  objects,  it  can  be 
taught  by  Illustrative  Teaching. 

(c)  The  numbers  to  be   added   together 
are  but  so  many  forms  for  the  aggre- 
gate of  many  smaller  parts,  having  no> 
logical  connection. 

(d)  The  subject-matter  is  represented  by 
certain     characters    called    Figures, 
which  are  arbitrary  in  their  form,  and 
have  no  logical  connection  with  each 
other. 

2.  Concerning  the  faculties  of  mind  that  are 
primarily  active  in  learning  addition  : 

(a)  The  Perceptive  faculties  are  required 
to   note,   intuitively,  the   individuals 
that  are  presented  to  them. 

(b)  Discrimination,   or  Comparison,   dis- 
tinguishes one  individual  in  Conscious- 
ness from  another. 

(c)  Memory  in  general,  or,  according  to* 
Hamilton,   Retentiveness    (or   Mem- 
ory), Recollection  (or  Reproduction), 
and  Representation,  preserves  for  fu- 
ture   use    the    knowledge    obtained 


230         ON    DISCOVERING   METHODS   OF 

through  Perception  and  Discrimina- 
tion. 

(d)  The  Power  of  Detecting  Identity,  or 
the    Power    of    Comparison,  or  the 
Power  of  Thought,  compares  or  iden- 
tifies what  may  come  within  Conscious- 
ness through  Perception,  with  what 
may  come  there  through  Memory. 

(e)  The  Power  of  expressing  Thought,  or 
Language. 

3.  Having  discovered  these  principles,  which 
are  the  Method  of  Teaching  addition,  he  pro- 
ceeds to  invent  his  Mode  of  Teaching  addition. 
This  Mode  may  be  by  illustration,  by  telling,  by 
questioning,  and  the  like. 

213.  He  regards  these  particular  points  :  1. 
To  what  degree  of  power  are  the  faculties  of  these 
children  grown  ?  2.  Is  this  System  of  Addition 
philosophically  constructed  ?  3.  In  what  quan- 
tity of  subject-matter  shall  the  points  of  the  sys- 
tem be  set  to  these  faculties  ?  He  may  write 
out  the  complete  lesson,  as  he  proposes  to  pre- 
sent it.  This  is  his  Mode.  He  may  then  ap- 
pear before  the  class  to  teach.  His  individual- 
ity, when  presenting  the  subject-matter,  exhibits 
his  Manner. 

The  only  guide  possible  for  procedure  in  the 
case  is  the  intelligence  of  the  teacher,  who  now 
invents  the  Mode.  If  there  be  deficiency  here, 
it  will  be  no  matter  for  surprise  if  the  children 
are  poorly  taught. 

"When  a  System  of  subject-matter  is  arranged 
in  detail  in  Modes  of  Teaching  it,  the  arrange- 


TEACHING  SPECIAL  SUBJECTS.          231 

ment  is  called  Methodical  All  methodical  dis- 
cussions for  teaching  must  rest  upon  Methods  of 
Teaching. 

214.  In  the  foregoing  procedure,  the  dis- 
covering of  the  Method  of  Teaching — the  process 
of  discovering  the  faculties,  and  the  nature  of 
the  subject-matter  that  is  to  be  adjusted  to  them, 
comprised  under  (1)  and  (2) — is  the  conception 
of  the  Science  of  Teaching. 

215.  The  Invention  of  the  Mode  of  Teaching, 
together   with  the  Manner  of  exhibiting  it  in 
practice,  is  the  conception  of  the  Art  of  Teach- 
ing. 

216.  The  Investigation  of  the  Science  and 
the  Art  of  Teaching  constitutes  the  Conception 
of  the  Profession  of  Teaching. 


III. 

CONCLUDING  REFLECTIONS. 

217.  Whatever  qualifications  of   mind    and 
person  the  teacher  may  have,  he  is  still  lacking 
in  a  most  important  element  of  success  if  he  has 
not  a  quick  apprehension  of  adopting  means  to 
«nds.     He  must  possess  versatility  of  powers  to 
discover  Methods  of  Teaching,  in  order  to  invent 
Modes  by  which  he  shall  incite  to  activity  the 
pupil's  mind   with   certainty.      To   do  this,  he 
needs  a  large  stock  of  "  That  unacquired,  un- 
bought,   untaught  sagacity,   which  certain  men 
have  by  nature,"  called  Common  Sense  or  good 
sense.    (McCosh,  Int.  of  Mind,  p.  93,  ed.  1870.) 
"  Common  Sense  is  the  spontaneous  action  of 
right  reason."    (M.  Bautain,  Art  of  Ext.  Speak- 
ing, ed.  1871.)     This  ability  is  needed  nowhere 
more  than  in  the  school-room,  and  he  who  lacks 
it  should  diligently  apply  himself  to  cultivating 
his  "  good  sense,"  if  he  would  attain  eminence 
in  the  Profession  of  Teaching. 

218.  "  An     open-eyed     and     open-minded 
physician  keeps  adding  to  his  knowledge  and 
altering  and  widening  his  theories  to  the  day  of 
his  death  ;  there  is  not  less  to  be  learned  in  the 
world  of  mind — in  the  world  of  the  school-room. 


CONCLUDING    REFLECTIONS.  233 

The  kind  of  teacher  who  stiffens  into 
the  school-master  misses  his  opportunities,  or  falls 
a  victim  to  that  arrestment  of  development  which 
has  overtaken  many  school  subjects,  and  which 
sometimes  overtakes  the  whole  of  school  life.'' 
(Meiklejohn,  Inaugural  Address,  Bell  Chair  of 
Education,  p.  11,  1876,  Edinburgh.) 

219.  "  Intellectually,  as  well  as  morally,  he 
(Arnold)  felt  that  the  teacher  ought  himself  to  be 
perpetually  learning,  and  so  constantly  above  the 
level  of  his  scholars.  '  I  am  sure,'  he  said, 
speaking  of  his  pupils  at  Laleham,  '  that  I  do 
not  judge  of  them  or  expect  of  them,  as  I  should,  if 
I  were  not  taking  pains  to  improve  my  own  mind. ' 
For  this  reason  he  maintained  that  no  school- 
master ought  to  remain  at  his  post  much  more 
than  fourteen  or  fifteen  years,  lest,  by  that  time, 
he  should  have  fallen  behind  the  scholarship  of 
the  age  ;  and  by  his  own  reading  and  literary 
works  he  endeavored  constantly  to  act  upon  this 
principle  himself.  4  The  dangers  '  (of 

falling  behind),  he  observed,  *  were  of  various 
kinds.  One  boy  may  acquire  a  contempt  for  the 
information  itself,  which  he  sees  possessed  by  a 
man  whom  he  feels  nevertheless  to  be  far  below 
him.  Another  (pupil)  will  fancy  himself  as 
much  above  nearly  all  the  world  as  he  feels  he  is 
above  his  own  tutor,  and  will  become  self-suffi- 
cient and  scornful.  A  third  will  believe  it  to  be 
his  duty,  as  a  point  of  humility,  to  bring  himself 
down  intellectually  to  a  level  with  one  whom  he 
feels  bound  to  reverence  ;  and  thus  there  have 
been  instances  where  the  veneration  of  a  young 


234  CONCLUDING    REFLECTIONS. 

man  of  ability  for  a  teacher  of  small  powers  has 
been  like  a  millstone  round  the  neck  of  an  eagle. ' '  ' 
(Arnold,  Life  of,  p.  137,  ed.  1870.) 

220.  "  We    may    say    that    common   sense 
scarcely  claims  to  provide  more  than  rather  in- 
definite general   rules,    which  no  prudent   man 
should  neglect  without  giving  himself  a  reason 
for  doing  so.     Such  reasons  may  either  be  drawn 
from  one's  knowledge  of  some  peculiarities  in 
one's  nature,  or  from  the  experience  of  others 
whom  one  has  ground  for  believing  to  be  more 
like  oneself  than  the  average  of  mankind  are. 
For  though,   as  we  saw,   there  is  considerable 
risk  of  error  in  thus  appropriating  the  experience 
of  others — and  in  fact  the  expression  of  it  will 
sometimes  appear  to  be  as  hesitating  and  contra- 
dictory as  the  judgments  of  common  sense — we 
may  extract  from  it  counsel  sufficiently  consist- 
ent   and    authoritative  to    supplement   at   least 
roughly  the  deficiencies  of  our  own  empirical 
generalizations. ' '     (Sidgwick,  Methods  of  Ethics, 
p.  145,  ed.  1874.) 

221.  "  But  many  who  allow  the  use  of  sys- 
tematic principles  in  other  things,  are  accustomed 
to  cry  up  Common-Sense  as  the  sufficient  and 
only  safe  guide  in  Reasoning.     Now  by  Common- 
Sense  is  meant,  I  apprehend,  (when  the  term  is 
used  with  any  distinct  meaning,)  an  exercise  of 
the  judgment  unaided  by  any  Art  or  system  of 
rules  :  such  an  exercise  as  we  must  necessarily 
employ  in  numberless  cases  of  daily  occurrence  ; 
in    which,  having   no    established   principles   to 
guide  us, — no  line  of  procedure,  as  it  were,  dis- 


CONCLUDING    REFLECTIONS.  235 

tinctly  chalked  out — we  must  needs  act  on  the 
best  extemporaneous  conjectures  we  can  form. 
He  who  is  eminently  skilful  in  doing  this,  is  said 
to  possess .  a  superior  degree  of  Common-Sense. 
But  that  Common-Sense  is  only  our  second  best 
guide — that  the  rules  of  Art,  if  judiciously 
framed  are  always  desirable  when  they  can  be 
had,  is  an  assertion,  for  the  truth  of  which  I  may 
appeal  to  the  testimony  of  mankind  in  general  ; 
which  is  so  much  the  more  valuable,  inasmuch 
as  it  may  be  accounted  the  testimony  of  adver- 
saries. For  the  generality  have  a  strong  predi- 
lection in  favor  of  Common- Sense,  except  in 
those  points  in  which  they,  respectively,  possess 
the  knowledge  of  a  system  of  rules  ;  but  in  these 
points  they  deride  any  one  who  trusts  to  unaided 
Common-Sense.  "  A  sailor  e.g.  will,  perhaps, 
despise  the  pretensions  of  medical  men,  and 
prefer  treating  a  disease  by  Common-Sense  :  but 
he  would  ridicule  the  proposal  of  navigating  a 
ship  by  Common-Sense,  without  regard  to  the 
maxims  of  nautical  art.  A  physician,  again, 
will  perhaps  contemn  Systems  of  Political- 
Economy,  of  Logic,  or  Metaphysics,  and  insist 
on  the  superior  wisdom  of  trusting  to  Common- 
Sense  in  such  matters  ;  but  he  would  never  ap- 
prove of  trusting  to  Common-Sense  in  the  treat- 
ment of  diseases. 

"  Neither,  again,  would  the  Architect  recom- 
mend a  reliance  on  Common-Sense  alone,  in  build- 
ing, nor  a  Musician,  in  music,  to  the  neglect  of 
those  systems  of  rules,  which,  in  their  respective 
arts  have  been  deduced  from  scientific  reason- 


236  CONCLUDING    REFLECTIONS. 

ing  aided  by  experience.  And  the  induction 
might  be  extended  to  every  department  of  prac- 
tice. Since,  therefore,  each  gives  the  preference 
to  unassisted  Common- Sense  only  in  those  cases 
where  he  himself  has  nothing  else  to  trust  to, 
and  invariably  resorts  to  the  rules  of  art,  wher- 
ever he  possesses  the  knowledge  of  them,  it  is 
plain  that  mankind  universally  bear  their  testi- 
mony, though  unconsciously  and  often  unwill- 
ingly, to  the  preferableness  of  systematic  knowl- 
edge to  conjectural  judgments. 

"  There  is,  however,  abundant  room  for  the 
employment  of  Common-Sense  in  the  application 
of  the  system.  To  bring  arguments  out  of  the 
form  in  which  they  are  expressed  in  conversation 
and  in  books,  into  the  regular  logical  shape,  must 
be  of  course,  the  business  of  Common-Sense, 
aided  by  practice,  for  such  arguments  are,  by 
supposition,  not  as  yet  within  the  province  of 
science."  (Whately,  Elements  of  Logic,  1859, 
pp.  xi.-xii.  of  Preface.) 

222.  •"  The  one  talent  which  is  worth  all 
other  talents  put  together  in  all  human  affairs  is 
the  talent  of  judging  right  upon  imperfect  ma- 
terials, the  talent  if  you  please  of  guessing 
right.  It  is  a  talent  which  no  rules  will  ever 
teach  and  which  even  experience  does  not  al- 
ways give.  It  often  coexists  with  a  good  deal 
of  slowness  and  dulness  and  with  a  very  slight 
power  of  expression.  All  that  can  be  said  about 
it  is,  that  to  see  things  as  they  are,  without  exag- 
geration or  passion,  is  essential  to  it ;  but  how 
can  we  see  things  as  they  are  ?  Simply  by  open- 


CONCLUDING    REFLECTIONS.  237 

ing  our  eyes  and  looking  with  whatever  power 
we  may  have.7'  (Stephen,  Liberty,  Equality, 
Fraternity,  p.  352,  ed.  1874,  London.) 

223.  "  The  assumed   logical   perfection    of 
thought  bears  about  the  same  relation  to  the  or- 
dinary state  of  the  human  mind  as  the  assump- 
tion of  perfectly  rigid  levers  and  perfectly  flexible 
cords  bears  in  the  action  of  those  instruments  in 
practice.    But,  on  the  other  hand,  the  possibility 
of  making  such  allowances  implies  that  the  differ- 
ence between  practice  and  theory  is  one  of  de- 
gree only,  and  not  of  kind.     The  instrument  as 
used  may  not  be  identical  with  the  instrument 
as  contemplated,  but  it  must  be  supposed  cap- 
able of   approximation  to  it."      (Mansel,  Prol. 
Log.,  p.  17.) 

224.  "  It  is  a  common  notion,  or  at  least  it 
is  implied  in  many  common  modes  of  speech, 
that  the  thoughts,  feelings,  and  actions  of  sen- 
tient beings  are  not  a  subject  of  science,  in  the 
same  strict  sense  in  which  this  is  true  of  the  ob- 
jects of  outward  nature.     This  notion  seems  to 
involve   some  confusion  of    ideas,    which  it  is 
necessary  to  begin  by  clearing  up.     Any  facts 
are   fitted,   in  themselves,   to    be  a  subject  of 
science  which  follow  one  another  according  to 
constant  laws,  although  those  laws  may  not  have 
been  discovered,  nor  even  be  discoverable  by  our 
existing  resources.     .     .     .     Scientific  inquiry 
has  not  yet  succeeded  in  ascertaining  the  order 
of  antecedence  and  consequence  among  phenom- 
ena, so  as  to^be  able,  at  least  in  our  regions  of 
the  earth,   to  predict  them   with  certainty,    or 


238  CONCLUDING    REFLECTIONS. 

even  with  a  high  degree  of  probability.  .  .  . 
But  meteorology  not  only  has  in  itself  every 
natural  requisite  for  being,  but  actually  is,  a 
science  ;  though  the  science  is  extremely  imper- 
fect. ...  No  one  doubts  that  Tidology 
(as  Dr.  Whewell  proposes  to  call  it)  is  really  a 
science.  .  .  But  circumstances  of  a  local  or  casual 
nature,  such  as  the  configuration  of  the  bottom 
of  the  ocean,  the  degree  of  confinement  from 
shores,  the  direction  of  the  wind,  etc. ,  influence, 
in  many  or  all  places,  the  height  and  time  of 
the  tide  ;  and  a  portion  of  these  circumstances  be- 
ing either  not  accurately  knowable,  not  precisely 
measurable,  or  not  capable  of  being  certainly 
foreseen,  the  tide  in  known  places  commonly 
varies  from  the  calculated  result  of  general  prin- 
ciples by  some  difference  that  we  are  not  able  to 
foresee-  or  conjecture.  .  .  .  And  this  is  what 
is  or  ought  to  be  meant  by  those  who  speak  of 
sciences  which  are  not  exact  sciences.  As- 
tronomy was  once  a  science,  without  being  an 
exact  science.  ...  It  has  become  an  exact 
science.  .  .  .  The  science  of  human  nature 
is  of  this  description.  It  falls  far  short  of  the 
standard  of  exactness  now  realized  in  Astron- 
omy ;  but  there  is  no  reason  that  it  should  not  be 
as  much  a  science  as  Tidology  is,  or  as  Astronomy 
was  when  its  calculations  had  only  mastered  the 
main  phenomena,  but  not  the  perturbations. 

"  The  phenomena  with  which  this  science  of 
(human)  nature  is  conversant  being  the  thoughts, 
feelings,  and  actions  of  human  beings,  it  would 
have  attained  the  ideal  perfection  of  a  science  if 


CONCLUDING    REFLECTIONS.  239 

it  enabled  us  to  foretell  how  an  individual  would 
think,  feel,  or  act  throughout  life,  with  the  same 
certainty  with  which  astronomy  enables  us  to  pre- 
dict the  places  and  the  occultations  of  the  heavenly 
bodies.  It  need  scarcely  be  stated  that  nothing 
approaching  to  this  can  be  done.  The  actions  of 
individuals  could  not  be  predicted  with  scientific 
accuracy,  were  it  only  because  we  can  not  fore- 
see the  whole  of  the  circumstances  in  which  those 
individuals  will  be  placed.  But  further,  even  in 
any  given  combination  of  (present)  circum- 
stances, no  assertion,  which  is  both  precise  and 
universally  true,  can  be  made  respecting  the 
manner  in  which  human  beings  will  think,  feel, 
and  act.  This  is  not,  however,  because  every 
person's  modes  of  thinking,  feeling,  and  acting 
do  not  depend  on  causes  ;  nor  can  we  doubt  that 
if,  in  the  case  of  any  individual,  our  data  could 
be  complete,  we  even  now  know  enough  of  the 
ultimate  laws  by  which  mental  phenomena  are 
determined,  to  enable  us  in  many  cases  to  pre- 
dict, with  tolerable  certainty,  what,  in  the 
greater  number  of  supposable  combinations  of 
circumstances,  his  conduct  or  sentiments  would 
be.  But  the  impressions  and  actions  of  human 
beings  are  not  solely  the  result  of  their  present 
circumstances,  but  the  joint  result  of  those  cir- 
cumstances and  of  the  characters  of  the  individ- 
uals ;  and  the  agencies  which  determine  human 
character  are  so  numerous  and  diversified  (noth- 
ing which  has  happened  to  the  person  through- 
out life  being  without  its  portion  of  influence), 


240  CONCLUDING    REFLECTIONS. 

that  in  the  aggregate  they  are  never  in  any  two 
cases  exactly  similar.  Hence,  even  if  our  science 
of  human  nature  were  theoretically  perfect,  that 
is,  if  we  could  calculate  any  character  as  we  can 
calculate  the  orbit  of  any  planet,  from  given  data ; 
still,  as  the  data  are  never  all  given,  nor  ever 
precisely  alike  in  different  cases,  we  could  neither 
make  positive  predictions,  nor  lay  down  univer- 
sal propositions. 

1  i  Inasmuch,  however,  as  many  of  those  effects 
which  it  is  of  most  importance  to  render  amena- 
ble to  human  foresight  and  control  are  deter- 
mined, like  the  tides,  in  an  incomparably  greater 
degree  by  general  causes,  than  by  all  partial  causes 
taken  together  ;  depending  in  the  main  on  those 
circumstances  and  qualities  which  are  common 
to  all  mankind,  or  at  least  to  large  bodies  of 
them,  and  only  in  a  small  degree  on  the  idiosyn- 
crasies of  organization  or  the  peculiar  history  of 
individuals  ;  it  is  evidently  possible  with  regard 
to  all  such  effects,  to  make  predictions  which 
will  almost  always  be  verified,  and  general  pro- 
positions which  are  almost  always  true.  And 
whenever  it  is  sufficient  to  know  how  the  great 
majority  of  the  human  race,  or  of  some  nation 
or  class  of  persons,  will  think,  feel,  and  act,  these 
propositions  are  equivalent  to  universal  ones. 
For  the  purpose  of  political  and  social  science 
this  is  sufficient.  As  we  formerly  remarked,  an 
approximate  generalization  is,  in  social  inquiries, 
for  most  practical  purposes  equivalent  to  an  exact 
one  ;  that  which  is  only  probable  when  asserted 


CONCLUDING    REFLECTIONS.  241 

of  individual  human  beings  indiscriminately  se- 
lected, being  certain  when  affirmed  of  the  char- 
acter and  collective  conduct  of  masses. 

"  It  is  no  disparagement,  therefore,  to  the 
science  of  Human  Nature,  that  those  of  its  gen- 
eral propositions  which  descend  sufficiently  into 
detail  to  serve  as  a  foundation  for  predicting 
phenomena  in  the  concrete,  are  for  the  most  part 
only  approximately  true.  But  in  order  to  give 
a  genuinely  scientific  character  to  the  study,  it 
is  indispensable  that  these  approximate  generali- 
zations, which  in  themselves  would  amount  only 
to  the  lowest  kind  of  empirical  laws,  should  be 
connected  deductively  with  the  laws  of  nature 
from  which  they  result  ;  should  be  resolved 
into  the  properties  of  the  causes  on  which  the 
phenomena  depend.  In  other  words,  the  science 
of  Human  Nature  may  be  said  to  exist  in  propor- 
tion as  the  approximate  truths,  which  compose 
a  practical  knowledge  of  mankind,  can  be  ex- 
hibited as  corollaries  from  the  universal  laws  of 
human  nature  on  which  they  rest  ;  whereby  the 
proper  limits  of  those  approximate  truths  would 
be  shown,  and  we  should  be  enabled  to  deduce 
others  for  any  new  state  of  circumstances,  in  an- 
ticipation of  specific  experience.  .  .  .  The 
proposition  now  stated  is  the  text  on  which  are 
based  the  '  Laws  of  Mind, '  and  *  Ethology,  or  the 
science  of  the  Formation  of  Character. '  '  '  (Mill, 
System  of  Logic,  pp.  586-596,  8°  ed.  1874.) 


APPENDIX   OF   QUOTATIONS. 

SECTION  PAGE 

225.  Appendix  A.— On  Method 348 

226.  B.— OnSystem 376 

227.  C.— On  Analysis 380 

228.  D.— On  Synthesis  383 

229.  E.— On  Definition 385 

230.  F.— On  Abstraction 390 

231.  G.— On  Generalization 392 

232.  H.— On  Classification 398 

233.  I.— On  Induction 413 

234.  J.— On  Interpretation 473 

235.  K.— On  Deduction ..  478 


APPENDIX  A. 

225.  EXTRACTS   SHOWING   THE   USE    OF    THE 
TERM  METHOD. 

1.  From  Hedge's  Logick,  ed.  1854,  pp.  149- 
150. 

Method,  in  logick,  is  a  proper  classification  and 
arrangement  of  our  thoughts  on  any  subject, 
either  to  facilitate  the  discovery  of  new  truths, 
or  to  assist  us  in  communicating  to  others  truths 
already  known  ;  or,  lastly,  to  enable  us  to  preserve 
for  future  use  the  knowledge,  which  we  have  ac- 
quired. The  disposition  best  adapted  to  the  in- 
vestigation of  truth  is  the  analytick  method; 
which  is  therefore  denominated  the  method  of 
invention ;  and  that  which  is  best  suited  to  the 
communication  of  knowledge,  is  the  synthetick 
method,  which  for  this  reason  has  been  called 
the  method  of  instruction.  In  both  of  these 
methods,  ideas  are  arranged  in  such  order,  as 
to  exhibit  their  mutual  connexions  and  relations. 

2.  'FromCoipipeQ'sMements  of  Logic,  ed.  1860, 
pp.  23-25. 

Method  is  the  order  and  arrangement  of  facts 
to  produce  a  certain  result  ;  to  establish  new 
truth,  to  investigate  old,  and  to  explain  and  teach 
both.  It  is  derived  from  the  Greek  jted'odov  $ 


246  APPENDIX   A. 

which  denotes  the  way  through  which  we  arrive 
at  a  certain  result. 

Whatever  steps  are  taken  to  make  knowledge 
profitable,  to  reduce  theory  to  practice,  and  to 
give  clear  and  intelligible  ideas  of  science,  con- 
stitute Method.  The  extension  of  the  term 
Method,  it  is  evident,  will  differ  according  to 
the  subject  to  which  it  is  applied. 

The  methods  of  investigation  differ  slightly 
for  the  different  kinds  of  science,  but  may  gen- 
erally be  classified  under  two  heads,  Analysis 
and  Synthesis,  of  which  the  former  is  generally 
used  in  the  private  investigation  of  truth,  and 
the  latter  for  the  purposes  of  instruction.  .  .  . 
We  speak  of  the  Method  of  a  single  science, 
or  a  Method  which  is  applied  to  all — as  in  that 
which  leads  to  the  Classification  of  the  sciences. 
In  either  investigation  the  division  of  Method 
into  Analysis  and  Synthesis,  is  a  just  one,  as 
both  are  used  in  either  process. 

3.  From  Day's  Elements  of  Logic,  ed.  1868, 
pp.  132-133. 

"Method  in  general  is  the  regulated  procedure 
towards  a  certain  end  ;  that  is,  a  process  governed 
by  rules,  which  guide  us  by  the  shortest  way 
straight  towards  a  certain  point,  and  guard  us 
against  devious  aberrations.  Now  the  end  of 
Thought  is  Truth,  Knowledge,  Science — expres- 
sions which  may  here  be  considered  as  convert- 
ible. Science,  therefore,  may  be  regarded  as  the 
perfection  of  thought,  and  to  the  accomplishment 
of  this  perfection  the  Methodology  of  Logic 
must  be  accommodated  and  be  conducive. ' ' 


APPENDIX  A.  247 

But  while  Science,  thus,  is  the  proper  end 
of  all  Thought,  and  Logical  Method  must  have 
reference  to  Thought  as  its  one  end,  it  is  still  to 
be  regarded  only  as  the  immediate  end,  which 
may,  itself,  be  modified  and  controlled  by  still 
higher  ends.  In  fact,  Science  or  Truth  may 
have  its  end  either  in  itself — in  the  True,  or 
in  the  Beautiful,  or  in  the  Right  and  Good  ; 
and  the  Method  of  Thought  will  vary  in  some 
respects  with  this  specific  remoter  end.  Still 
further,  the  Method  of  Thought  will  vary  with 
the  more  specific  ends  under  each  of  these  higher 
governing  ends.  We  may  deal  with  Thought  for 
the  purpose  of  acquiring  knowledge,  or  for  the 
purpose  of  communicating  knowledge  ;  and  the 
Method  requisite  for  the  Investigation  of  Truth 
will  so  far  vary  from  the  Method  requisite  for 
the  Communication  of  Truth. 

In  like  manner  the  Method  of  Thought,  as- 
governed  by  the  higher  end  of  guiding  to  the 
Beautiful,  will  vary  specifically,  as  the  particular 
end  is  the  Contemplation  or  the  Creation  of  the 
Beautiful. 

So,  too,  we  have  a  specific  variation  in  the 
Method  of  Thought,  where  the  governing  idea  is 
the  Right  or  the  Good,  according  as  Subjective 
or  Objective  Rectitude  or  Goodness  is  the  partic- 
ular end. 

It  is  sufficient  to  point  out  here  these  modi- 
fications of  Logical  Method  in  respect  to  these 
several  general  ends  in  thinking.  The  full,  de- 
tailed consideration  of  them  belongs  either  to 
modified  Logic  or  to  Applied  or  Special  Logic. 


248      .  APPENDIX   A. 

Pure  Logic  confines  itself  to  the  domain  of  Truth 
in  itself — Science  for  its  own  sake. 

4.  From  Fleming's  Vocabulary  of  Philosophy, 
ed.  1858,  pp.  316-319. 

Method  means  the  way  or  path  by  which  we 
proceed  to  the  attainment  of  some  object  or  aim. 
In  its  widest  acceptation,  it  denotes  the  means 
employed  to  obtain  some  end.  Every  art  and 
every  handicraft  has  its  method. 

Scientific  or  philosophical  method  is  the  march 
which  the  mind  follows  in  ascertaining  or  com- 
municating truth.  It  is  the  putting  of  our 
thoughts  in  a  certain  order  with  a  view  to  im- 
prove our  knowledge  or  to  convey  it  to  others. 

Method  may  be  called,  in  general,  the  art 
of  disposing  well  a  series  of  many  thoughts, 
either  for  the  discovering  truth  when  we  are 
ignorant  of  it,  or  for  proving  it  to  others  when 
it  is  already  known.  Thus  there  are  two  kinds 
of  method,  one  for  discovering  truth,  which  is 
called  analysis,  or  the  method  of  resolution,  and 
which  may  also  be  called  the  method  of  inven- 
tion ;  and  the  other  for  explaining  it  to  others 
when  we  have  found  it,  which  is  called  synthesis, 
or  the  method  of  composition,  and  which  may 
also  be  called  the  method  of  doctrine.  (Port 
Boy.  Logic,  Part  IV.,  ch.  2.) 

"Method,  which  is  usually  described  as  the 
fourth  part  of  Logic,  is  rather  a  complete  prac- 
tical Logic.  It  is  rather  a  power  or  spirit  of  the 
intellect,  pervading  all  that  it  does,  than  its  tan- 
gible product."  (Thomson,  Outline  of  Laws 
of  Thought,  sect.  119.) 


APPENDIX   A.  249 

Every  department  of  philosophy  has  its  own 
proper  method ;  but  there  is  a  universal  method 
or  science  of  method.  This  was  called  by  Plato, 
dialectic  ;  and  represented  as  leading  to  the  true 
and  real.  (Repub.,  lib.  vii.)  It  has  been  said 
that  the  word  /*£0odo£,  as  it  occurs  in  Aris- 
totle's Ethics,  should  be  translated  '  systems/ 
rather  than  '  method.' — (Paul,  Analysis  of  Aris- 
totle9 s  Ethics,  p.  1.)  But  the  construction  of 
a  system  implies  method.  And  no  one  was  more 
thoroughly  aware  of  the  importance  of  a  right 
method  than  Aristotle.  He  has  said  (Metaphys. , 
lib.  ii.),  u  that  we  ought  to  see  well  what  demon- 
stration (or  proof)  suits  each  particular  subject  ; 
for  it  would  be  absurd  to  mix  together  the  re- 
search of  science  and  that  of  method;  two 
things,  the  acquisition  of  which  offers  great  diffi- 
culty." The  deductive  method  of  philosophy 
came  at  once  finished  from  his  hand.  And  the 
inductive  method  was  more  extensively  and  suc- 
cessfully followed  out  by  him  than  has  been  gen- 
erally thought. 

James  Acontius,  or  Concio,  as  he  is  sometimes 
called,  was  born  at  Trent,  and  came  to  England 
in  1567.  He  published  a  work,  De  Methodo. 
.  .  .  According  to  him  all  knowledge  de- 
duced from  a  process  of  reasoning  presupposes 
some  primitive  truths,  founded  in  the  nature  of 
man,  and  admitted  as  soon  as  announced  ;  and 
the  great  aim  of  method  should  be  to  bring  these 
primitive  truths  to  light,  that  by  their  light  we 
may  have  more  light.  Truths  obtained  by  the 


250  APPEKDIX  A. 

senses,  and  by  repeated  experience,  become  at 
length  positive  and  certain  knowledge. 

Descartes  has  a  discourse  on  Method.  He 
has  reduced  it  to  four  general  rules. 

I.  To   admit   nothing  as    true   of  which  we 
have  not  a  clear  and  distinct  idea.     We  have  a 
clear  and  distinct  idea  of  our  own  existence. 
And  in  proportion  as  our  idea  of  anything  else 
approaches  to,  or  recedes  from,  the  clearness  of 
this  idea,  it  ought  to  be  received  or  rejected. 

II.  To  divide   every  object  inquired  into  as 
much  as  possible  into  its  parts.     Nothing  is  more 
simple  than  the  ego,  or  self-consciousness.     In 
proportion  as  the  object  of  inquiry  is  simplified, 
the  evidence  comes  to  be  nearer  that  of  self- 
consciousness. 

III.  To  ascend  from  simple  ideas  or  cogni- 
tions to  those  that  are  more  complex.     The  real 
is  often  complex  :  and  to  arrive  at  the  knowledge 
of  it  as  a  reality,  we  must  by  synthesis  reunite 
the  parts  which  were  previously  separated. 

IV.  By  careful  and  repeated  enumeration  to 
see  that  all  the  parts  are  reunited.     For  the  syn- 
thesis will  be  deceitful  and  incomplete  if  it  do 
not  reunite  the  whole,  and  thus  give  the  reality. 

This  method  begins  with  provisory  doubt, 
proceeds  by  analysis  and  synthesis,  and  ends  by 
accepting  evidence  in  proportion  as  it  resembles 
the  evidence  of  self-consciousness. 

These  rules  are  useful  in  all  departments 
of  philosophy.  But  different  sciences  have 
different  methods  suited  to  their  objects  and  to 
the  end  in  view. 


APPENDIX   A.  251 

In  prosecuting  science  with  the  view  of  ex- 
tending our  knowledge  of  it,  or  the  limits  of  it, 
we  are  said  to  follow  the  method  of  investigation 
or  inquiry,  and  our  procedure  will  be  chiefly  in 
the  way  of  analysis.  But  in  communicating 
what  is  already  known,  we  follow  the  method  of 
exposition  or  doctrines,  and  our  procedure  will 
be  chiefly  in  the  way  of  synthesis. 

In  some  sciences  the  principles  or  laws  are 
given,  and  the  object  of  the  science  is  to  discover 
the  possible  application  of  them.  In  these  sci- 
ences the  method  is  deductive,  as  in  geometry. 
In  other  sciences,  the  facts  or  phenomena  are 
given,  and  the  object  of  the  science  is  to  dis- 
cover the  principles  or  laws.  In  these  sciences 
the  proper  method  is  inductive,  proceeding  by 
observation  or  experiment,  as  in  psychology  and 
physics.  The  method  opposed  to  this,  and 
which  was  long  followed,  was  the  constructive 
method ;  which,  instead  of  discovering  causes  by 
induction,  imagined  or  assigned  them  a  priori, 
or  ex  hypothesij  and  afterwards  tried  to  verify 
them.  This  method  is  seductive  and  bold  but 
dangerous  and  insecure,  and  should  be  resorted 
to  with  great  caution. 

The  use  of  method,  both  in  obtaining  and 
applying  knowledge  for  ourselves,  and  in  convey- 
ing and  communicating  it  to  others,  is  great  and 
obvious. 

"  Marshal  thy  notions  into  a  handsome  meth- 
od. One  will  carry  twice  as  much  weight, 
trussed  and  packed  up  in  bundles,  than  when  it 
lies  untoward,  flapping,  and  hanging  about  his 


252  PPEKDIX   A. 

shoulders."      (Pleasures   of    Literature    12mo, 
Lond.,  1851,  p.  104.) 

5.  From  Preface  of  "  A  Brief  English  Gram- 
mar on  a  Logical  Method,"  by  Alexander  Bain, 

The  chief  peculiarity  in  the  plan  of  the  pres- 
ent work  lies  in  anticipating  the  unavoidable 
difficulties  of  the  subject  by  a  previous  handling 
of  certain  elementary  notions  (belonging  to  all 
science),  without  which  no  one  can  hope  to  un- 
derstand the  scope  or  method  of  grammar. 
After  such  preliminary  explanations,  I 
make  no  scruple  to  introduce  a  strict  mode  of 
defining  the  Parts  of  Speech.  I  also  exemplify 
the  leading  subdivisions  or  classes  of  each. 
Moreover,  I  bring  forward  at  once  the  equivalent 
phrases,  which,  in  the  case  of  the  Adverb  in  par- 
ticular, are  used  more  frequently  than  single 
words.  On  this  method,  the  Grammatical  pars- 
ing of  a  sentence  directs  attention  forcibly  to  the 
meaning.  ...  It  (the  Key)  also  includes  a 
large  selection  of  additional  examples,  which  are 
commented  on  with  a  view  to  set  forth  still  far- 
ther the  methods  of  parsing,  and  to  illustrate 
the  constructions  and  idioms  of  the  language. 

6.  From  WhewelFs  Novum  Organon  Renova- 
tum,ed.  1858,  pp.  141-144. 

The  name  Organon  was  applied  to  the  works 
of  Aristotle  which  treated  of  Logic,  i.e.,  of  the 
method  of  establishing  and  proving  knowledge, 
and  of  refuting  errour,  by  means  of  Syllogisms. 
Francis  Bacon,  holding  that  this  method  was  in- 
sufficient for  the  augmentation  of  real  knowl- 
edge, published  his  Novum  Organon  in  which  he 


APPENDIX   A.  253 

proposed  for  that  purpose  methods  from  which 
he  promised  a  better  success,  (p.  3.) 

The  Methods  by  which  the  construction  of 
Science  is  promoted  are,  Methods  of  Observa- 
tion, Methods  of  obtaining  clear  Ideas,  and 
Methods  of  Induction. 

Aphorism  xxvii.  ...  I  shall,  therefore, 
attempt  to  resolve  the  Process  of  Discovery  into 
its  parts,  and  to  give  an  account  as  distinct  as  may 
be  of  Rules  and  Methods  which  belong  to  each 
portion  of  the  process. 

In  Book  II.  we  considered  the  three  main 
parts  of  the  process  by  which  science  is  con- 
structed :  namely,  the  Decomposition  and  Ob- 
servation of  Complex  Facts  ;  the  Explication  of 
our  Ideal  Conceptions  ;  and  the  Colligation  of 
Elementary  Facts  by  means  of  those  conceptions. 
The  first  and  last  of  these  three  steps  are  capable 
of  receiving  additional  accuracy  by  peculiar  pro- 
cesses. They  may  further  the  advance  of  science 
in  a  more  effectual  manner,  when  directed  by 
special  technical  Methods,  of  which  in  the  pres- 
ent book  we  must  give  a  brief  view.  In  this 
more  technical  form,  the  observation  of  facts  in- 
volves the  Measurement  of  Phenomena ;  and  the 
Colligation  of  Facts  includes  all  arts  and  rules  by 
which  the  process  of  Induction  can  be  assisted. 
Hence  we  shall  have  here  to  consider  Methods 
of  Observation,  and  Methods  of  Induction,  us- 
ing these  phrases  in  the  widest  sense.  The  sec- 
ond of  the  three  steps  above  mentioned,  the 
Explication  of  our  Conceptions,  does  not  admit 
of  being  much,  assisted  by  methods,  although 


254  APPENDIX   A. 

something  may  be  done  by  Education  and  Dis- 
cussion. 

The  Methods  of  Induction,  of  which  we  have 
to  speak,  apply  only  to  the  first  step  in  our 
ascent  from  phenomena  to  laws  of  Nature  ; — the 
discovery  of  Laws  of  Phenomena.  A  higher  and 
ulterior  step  remains  behind,  and  follow  in  natu- 
ral order  the  discovery  of  Laws  of  Phenomena  ; 
namely,  the  Discovery  of  Causes ;  and  this  must 
be  stated  as  a  distinct  and  essential  process  in  a 
complete  view  of  the  course  of  science.  Again, 
when  we  have  thus  ascended  to  the  causes  of 
phenomena  and  of  their  laws,  we  can  often  rea- 
son downwards  from  the  cause  so  discovered  ; 
and  we  are  thus  led  to  suggestions  of  new  phe- 
nomena, or  to  new  explanations  of  phenomena 
already  known.  Such  proceedings  may  be  termed 
Applications  of  our  discoveries  ;  including  in 
the  phrase,  Verifications  of  our  Doctrines  by 
such  an  application  of  them  to  observed  facts. 

Hence  we  have  the  following  series  of  pro- 
cesses concerned  in  the  formation  of  science. 

(1.)  Decomposition  of  Facts  ; 

(2.)  Measurement  of  Phenomena  ; 
Explication  of  Conceptions  ; 
Induction  of  Laws  of  Phenomena  ; 
Induction  of  Causes  ; 

)  Application  of  Inductive  Discoveries, 
f  these  six  processes,  the  methods  by  which 
the  second  and  fourth  may  be  assisted  are  here 
our  peculiar  object  of  attention.  The  treat- 
ment of  these  subjects  in  the  present  work  must 
necessarily  be  scanty  and  imperfect,  although  we 


APPENDIX   A.  255 

may  perhaps  be  able  to  add  something  to  what 
has  hitherto  been  systematically  taught  on  these 
heads.  Methods  of  Observation  and  of  Induc- 
tion might  of  themselves  form  an  abundant  sub- 
ject for  a  treatise,  and  hereafter  probably  will  do 
so,  in  the  hands  of  future  writers.  A  few  re- 
marks, offered  as  contributions  on  this  subject, 
may  serve  to  show  how  extensive  it  is,  and  how 
much  more  ready  it  now  is  than  it  ever  before 
was,  for  a  systematic  discussion. 

Of  the  above  steps  of  the  formation  of  sci- 
ence, the  first,  the  Decomposition  of  Facts,  has 
already  been  sufficiently  explained  in  the  last 
Book  :  for  if  we  pursue  it  into  further  detail  and 
exactitude,  we  find  that  we  gradually  trench  upon 
some  of  the  succeeding  parts.  I,  therefore,  pro- 
ceed to  treat  of  the  second  step,  the  Measure- 
ment of  Phenomena  ; — of  Methods  by  which 
this  work,  in  its  widest  sense,  is  executed,  and 
these  I  shall  term  Methods  of  Observation. 

7.  From  Bowen's  Logic,  ed.  1874,  pp.  30-38. 

Logic  is  the  Science  of  the  Necessary  Laws  of 
Pure  Thought,  .  .  .  that  is,  it  treats  of 
Language  so  far  only  as  this  is  the  vehicle  of 
Thought.  Just  the  reverse  is  true  of  the  science 
of  Grammar,  which  treats  primarily  of  Language, 
and  only  secondarily  of  Thought.  Logic  might 
be  called  the  Grammar  of  Thought.  . 
Pure,  or,  as  it  is  sometimes  termed,  Formal 
Thought,  is  the  mere  process  of  thinking,  irre- 
spective of  what  we  are  thinking  about.  It 
has  already  been  said  that  the  Acquisitive  or 
Perceptive  Faculty  furnishes  "  the  Matter,"  while 


256  APPENDIX   A. 

the  Understanding  supplies  "  the  Form,"  of  our 
knowledge.  This  distinction  between  Matter 
and  Form  is  one  of  considerable  importance  in 
the  history  of  philosophy.  The  former  is  the 
crude  material  or  the  stuff  of  which  anything 
consists,  or  out  of  which  it  is  made  ;  while  the 
latter  is  the  peculiar  shape  or  modification  given 
to  it  by  the  artist,  whereby  it  has  become  this 
particular  thing  which  it  is,  and  not  something 
else  which  might  have  been  fashioned  out  of  the 
same  substance.  Thus,  wood  is  the  Matter  of 
the  desk  on  which  I  am  writing,  whilst  the  Form 
is  that  which  entitles  it  to  be  called  a  desk,  rather 
than  a  table  or  a  chair.  Vocal  sound  is  the 
Matter,  of  speech,  and  articulation  is  its  Form. 
It  is  evident  that  these  are  two  correlative  no- 
tions, each  of  which  implies  the  other  :  Matter 
cannot  exist  except  under  some  Form,  and  there 
cannot  be  any  Form  except  of  some  given  Mat- 
ter. But  though  the  two  cannot  actually  be  sep- 
arated, the  mind  can  consider  each  separately 
through  that  process,  called  abstraction,  whereby 
the  attention  is  wholly  given  to  the  one  to  the 
exclusion  of  the  other.  We  may  think  sepa- 
rately of  the  attributes  which  are  common  to  a 
whole  class  of  Forms,  disregarding  altogether, 
for  the  moment,  the  Matter  of  which  each  of 
them  really  consists.  Borrowing  algebraic 
symbols,  the  Matter  in  each  case  may  be  desig- 
nated by  a  letter  of  the  alphabet,  the  peculiar 
significance  of  which  is,  that  it  stands  for  any 
Matter  whatever,  and  not  for  any  one  in  partic- 
ular. Thus,  A  is  B,  is  the  Form  of  an  affirma- 


APPENDIX   A.  257 

tive  judgment,  wherein  A  and  B  stand  for  any 
two  Concepts  whatever.  Hence,  whatever  is  true 
of  the  general  formula,  A  is  B,  will  be  true  also 
of  any  such  particular  instances,  as  Iron  is  mallea- 
ble, Trees  are  plants,  etc.,  wherein  the  Form  is 
associated  with  some  particular  Matter.  In  say- 
ing, then,  that  Logic  is  concerned  only  with  the 
Forms  of  Thought,  or  Pure  Thought,  or  Thought 
in  the  abstract, — for  all  these  expressions  signify 
the  same  thing, — we  mean  only,  that  what  is  Ma- 
terial in  Thought  is  extralogical,  and,  as  logi- 
cians, we  have  nothing  to  do  with  it  ;  just  as 
the  geometer  has  nothing  to  do  with  the  partic- 
ular diagram  on  the  paper  before  him,  except  sa 
far  as  it  is  a  symbol,  or  universal  Form,  of  all  pos- 
sible figures  of  the  same  general  character.  .  .  . 

Again,  the  definition  of  Logic  assumes  that 
the  process  of  Thinking,  like  every  other  opera- 
tion in  nature,  does  not  take  place  at  random, 
but  according  to  certain  fixed  Laws  or  invariable 
modes  of  procedure.  There  could  be  no  com- 
munication  of  Thought  from  one  mind  to  an- 
other, if  the  process  of  Thinking  in  all  minds 
were  not  subject  to  the  same  general  rules.  We 
follow  these  laws  for  the  most  part  unconscious- 
ly, as  a  distinct  recognition  of  them  is  not  by 
any  means  necessary  for  correct  thinking  ;  just 
so,  many  persons  speak  and  write  correctly 
without  any  knowledge  of  the  grammarian's 
rules.  .  .  . 

Properly  speaking,  Pure  Logic  terminates 
with  the  consideration  of  the  three  classes  of 
products — namely,  Concepts,  Judgments,  and 


258  APPENDIX   A. 

Reasonings — which  are  the  elements  into  which 
all  Thought  is  resolved.  But  Thought  itself  is 
subsidiary  to  the  attainment  of  knowledge, — that 
is,  to  Science.  The  question  remains,  then, 
after  we  have  fully  treated  of  Concepts,  Judg- 
ments, and  Reasonings,  taken  separately  or  con- 
sidered in  themselves  alone,  what  use  is  to  be 
made  of  them,  taken  together,  in  the  construc- 
tion of  Science.  A  full  answer  to  this  question, 
as  it  would  involve  a  study  of  the  objects  of 
Science, — that  is,  of  the  matter  of  the  special 
sciences, — evidently  falls  outside  of  the  province 
of  Logic.  But  a  partial  answer  to  it,  regarding 
Science  in  its  relation,  not  to  the  objects  known, 
but  to  the  knowing  mind,  may  be  considered  as 
a  natural  appendage  to  Logic,  as  it  embraces  the 
conditions  not  merely  of  possible,  but  of  perfect, 
Thought.  Such  an  answer  is  usually  called  the 
Doctrine  of  Method,  or  Logical  Methodology. 
Pure  Logic  considers  only  the  Necessary  Laws 
to  which  all  Thought  must  conform  ;  the  Doc- 
trine of  Method  regards  those  rules  and  princi- 
ples to  which  all  Thought  ought  to  conform  in 
order  to  obtain  its  end,  which  is  the  advance- 
ment of  Science.  Pure  Logic  treats  merely  of 
the  elements  of  Thought,  while  Logical  Method- 
ology regards  the  proper  arrangement  of  these 
elements  into  an  harmonious  whole.  All  Method 
is  a  well-defined  progress  towards  some  end  ; 
and  the  end  in  this  case  is  the  attainment  of 
truth.  Practically  speaking,  the  Doctrine  of 
Method  is  a  body  of  rules  or  precepts  looking  to 
the  proper  regulation  of  the  Thinking  Faculty 


QUOTATIONS   ON   METHOD.  259 

in  the  pursuit  of  knowledge  ;  and,  as  such,  it 
necessarily  lacks  the  precision  and  the  demon- 
strative certainty  which  are  characteristic  of  the 
principles  of  Pure  Logic.  The  laws  of  Pure 
Thought  are  absolute  ;  the  merits  of  Perfect 
Thought  are  various,  and  attainable  in  different 
degrees,  according  to  circumstances. 

Another  distinction  has  been  taken,  in  this 
science,  between  Pure  and  Applied  Logic,  or  as 
Sir  William  Hamilton  prefers  to  call  the  latter, 
Modified  Logic.  The  former,  as  we  have  seen, 
considers  the  Thinking  Faculty  alone,  as  if  it 
constituted  the  whole  of  the  human  mind,  and 
therefore  as  if  its  Laws  and  Products  were  unaf- 
fected by  any  collateral  and  disturbing  influences, 
but  were  manifested  in  precisely  the  same  man- 
ner by  different  persons.  It  takes  no  account  of 
the  defects  and  hinderances  which  obstruct  the 
normal  action  of  the  understanding.  Modified 
Logic,  on  the  other  hand,  considers  Thought  as 
it  is,  and  not  merely  as  it  ought  to  be.  It  re- 
gards ' i  the  Causes  of  Error  and  the  Impediments 
to  Truth  by  which  man  is  beset  in  the  employ- 
ment of  his  Faculties,  and  what  are  the  means 
of  their  removal."  And  yet  it  is  a  universal 
science, — as  much  so  as  Pure  Logic  ;— for  it 
does  not  consider  the  Matter  of  Thought.  . 
.  .  .  But  Modified  Logic  is  not  properly  called 
Logic,  as  it  is  a  branch  of  Psychology,  which 
treats  of  the  phenomena  of  mind  in  general,  and 
not  merely  of  the  normal  action  and  necessary 
laws  of  one  special  faculty,  the  Understanding. 
As  Modified  Logic,  however,  is  nearly  allied  in 


260  QUOTATIONS   OK   METHOD. 

purpose  with  the  Doctrine  of  Method,  both  look- 
ing to  the  same  general  end, — the  attainment  of 
truth  through  the  proper  regulation  of  the  Think- 
ing Faculty, — the  two  may  well  be  considered 
together,  under  the  general  name  of  Applied 
Logic,  as  a  kind  of  supplement  to  the  science 
properly  so  called. 

8.  From  Outlines  of  Ontological  Science,  by 
H.  N.  Day,  ed.  1878,  pp.  123  and  following. 

The  very  conception  of  method  involves,  to- 
gether with  something  that  changes,  a  source  or 
origin  from  which  the  change  begins  ;  an  end  or 
goal  in  which  it  rests  or  to  which  it  tends  ;  and 
a  way  by  which  the  end  is  reached  from  the  be- 
ginning. 

A  rational  method,  moreover,  implies  a  unity 
of  nature  and  imposes  a  unity  on  each  of 
the  fundamental  elements  of  true  method.  It 
prescribes  the  right  movement  from  some  single 
source,  to  some  single  end,  by  some  single  way. 
Its  function  is  discharged  when  it  indicates  this 
movement  and  directs  it  as  to  such  single  source, 
end,  and  way. 

We  have  found  in  all  knowledge  a  twofold,  a 
subjective  and  an  objective  element — a  knowing 
and  a  known.  A  rational  method  respects  the 
change  in  both  aspects.  At  every  stage  of  prog- 
ress, in  all  true  and  right  knowledge  the  corre- 
spondence between  these  two  constituents  is  main- 
tained perfect  and  exact.  The  subjective  con- 
stituent increases  by  the  growth  effected  through 
exercise  in  a  living  agent  ;  and  the  objective 
constituent  increases  in  exact  correspondence  ; — 


QUOTATIONS   ON   METHOD.  261 

the  capacity  of  knowing  is  enlarged  and  intensi- 
fied as  the  matter  known  is  broadened  and  deep- 
ened. The  view  of  method,  however,  will  be 
modified  according  as  the  one  or  the  other  of 
these  constituents  is  prominently  regarded.  We 
conveniently  distinguish,  accordingly,  a  subjec- 
tive and  an  objective  method  in  knowl- 
edge. .  .  . 

The  subjective  method  in  knowledge  respects- 
the  knowing  subject.  The  source  or  origin  here 
is  ever  the  knowing  power  or  function  itself  at 
each  of  the  ever  advancing  stages  of  its  progress. 

The  end  or  goal  is  primarily  the  perfection 
of  the  knowing  faculty,  and  through  that  the 
perfection,  according  to  its  nature,  of  the  whole 
organism  of  which  this  faculty  is  a  part  ; — a 
goal  ever  aimed  at,  but  never  reached  as  a  final 
knowing,  yet  in  each  specific  act  of  knowing 
attained  in  its  own  proper  degree  and  measure. 

The  way  is  by  a  continuous  endeavor  in  ac- 
cordance with  the  laws  of  thinking  or  knowing,  in, 
which  each  new  measure  of  thinking  energy  at- 
tained is  made  the  occasion  and  means  of  a  still 
more  vigorous  life  of  thought.  This  is  prescrib- 
ed by  the  principle  of  adjacence  ;  continuousness- 
is  but  progress  from  next  to  next  in  order  of 
proximity  or  adjacence. 

The  objective  method  in  knowledge  respects 
the  matter  known. 

The  beginning  in  knowledge  here  is  the  datum 
presented  to  thought.  This  datum  must  be  of 
the  nature  of  that  which  can  be  known  ; — must  be 
of  the  nature  of  truth.  Every  fresh  attainment 
of  truth  adds  so  much  to  the  volume  of  attain- 


262  QUOTATIONS   OK   METHOD. 

ment  which,  with  what  is  given  on  each  succes- 
sive occasion  of  thought,  constitutes  the  datum 
for  the  succeeding  stage. 

The  objective  end  in  knowledge  is  truth  ac- 
quired in  its  complete  fulness  and  comprehensive- 
ness— the  universe  of  truth  ; — an  end  never  fully 
reached,  yet  in  its  measure  attained  in  every  new 
acquisition. 

The  way  in  objective  knowledge  is  in  unde- 
viating  course  through  the  adjacent  fields  of  truth, 
from  boundary  through  to  boundary,  avoiding,  as 
far  as  may  be,  under  the  conditions  of  human 
life,  skips  and  divisions  and  devious  windings. 

9.  From  Comte's  Philosophy  of  the  Sciences, 
G.  H.  Lewes,  London,  1853. 

Atheists  may  therefore  be  regarded  as  the 
most  illogical  of  theologians,  since  they  attempt 
the  theological  problems  while  rejecting  the  only 
suitable  method,  (p.  25.) 

That  the  positive  Method  is  the  only  Method 
adapted  to  human  capacity,  the  only  one  on  which 
truth  can  be  found,  is  easily  proved  :  on  it  alone 
can  prevision  of  phenomena  depend,  (p.  39.) 

The  present  condition  of  science,  therefore, 
exhibits  three  ^lethods  instead  of  one  :  hence  the 
anarchy. 

To  remedy  the  evil,  all  differences  must  cease  : 
one  Method  must  preside,  (p.  38.) 

In  passing  from  one  science  to  another,  we 
discover  the  several  modifications  which  method 
(essentially  the  same  in  all)  undergoes. 

A  proper  knowledge  of  the  positive  method 
can  only  be  acquired  in  this  way.  (p.  49.) 

I  propose  to  call  the  relations  of  co-existence 


QUOTATIONS   ON   METHOD.  263 

and    succession,    usually   named    Laws,  by   the 
name  of  Methods. 

Etymologically,  Method  is  a  path  leading  on- 
wards, a  way  of  transit.  The  Methods  of  Na- 
ture would  therefore  express  the  paths  along 
which  the  activities  of  Nature  travelled  to  results 
(phenomena),  (p.  55.) 

What  we  call  Laws  are  nothing  but  the  paths, 
or  Methods,  along  which  the  Forces  (of  Nature) 
move.  (p.  57.) 

Astronomy  is  more  truly  scientific  and  has  at- 
tained the  highest  degree  of  philosophical  perfec- 
tion that  any  science  can  ever  pretend  to,  as  re-' 
spects  Method, — the  exact  reduction  of  all  phe- 
nomena, both  in  kind  and  in  degree,  to  one  gen- 
eral law  (solar  astronomy),  (p.  83.) 

A  law  of  Nature  can  only  be  discovered  by  In- 
duction or  Deduction.  Often,  however,  neither 
method  is  of  itself  sufficient,  (p.  105.) 

The  Methods  in  which  these  masses  (suns, 
planets,  etc.)  move,  science  attempts  to  ascer- 
tain ;  but  in  Astronomy  we  speak  of  Motion,  in 
Chemistry  of  Combination  ;  both  are  Methods  of 
the  unknown  unknowable  Force,  (p.  113.) 

The  methods  by  which  the  construction  of 
science  is  promoted  are,  Methods  of  Observation, 
Methods  of  obtaining  clear  Ideas,  and  Methods 
of  Instruction,  (p.  141.)  (Whewell.) 

The  methods  of  observation  of  quantity  in 
general  are,  Numeration,  which  is  precise  by  the 
nature  of  number  :  the  Measurement  of  Space 
and  Time,  by  which  aids  the  Measurement  of  the 
other  ;  the  Method  of  Repetition  ;  the  Method 
of  Coincidences  or  Interferences.  (p.  145.) 
(Whewell.) 


QUOTATIONS  ON  SYSTEM. 

APPENDIX    B. 

226.  From  Fleming — Vocabulary  of  Philos- 
ophy, ed.  1867. 

SYSTEM  is  a  full  and  connected  view  of  all  the 
truths  of  some  department  of  knowledge.  An 
organized  body  of  truth,  or  truths  arrange 
under  one  and  the  same  idea,  which  idea  is  as 
the  life  or  soul  which  assimilates  all  those  truths. 
No  truth  is  altogether  isolated.  Every  truth 
has  relation  to  some  other.  And  we  should 
try  to  unite  the  facts  of  our  knowledge  so  as  to 
see  them  in  their  several  bearings.  This  we  do 
when  we  frame  them  into  a  system.  To  do  so 
legitimately  we  must  begin  by  analysis  and  end 
with  synthesis.  But  system  applies  not  only  to 
our  knowledge,  but  to  the  objects  of  our  knowl- 
edge. Thus  we  speak  of  the  planetary  system, 
the  muscular  system,  the  nervous  system.  We 
believe  that  the  order  to  which  we  would  reduce 
our  ideas  has  a  foundation  in  the  nature  of 
things.  And  it  is  this  belief  that  encourages  us 
to  reduce  our  knowledge  of  things  into  a  system- 
atic order.  The  doing  so  is  attended  with  many 
advantages.  At  the  same  time  a  spirit  of  sys- 
tematizing may  be  carried  too  far.  It  is  only  in 
•so  far  as  it  is  in  accordance  with  the  order  of  na- 


QUOTATIONS   OK   SYSTEM.  265 

ture  that  it  can  be  useful  or  sound.  Condillac 
has  a  Traite  des  Systemes,  in  which  he  traces 
their  causes  and  their  dangerous  consequences. 

SYSTEM,  ECONOMY,  OR  CONSTITUTION.  —  "A 
System,  Economy,  or  Constitution,  is  a  one  or 
a  whole,  made  up  of  several  parts,  but  yet  that 
the  several  parts  even  considered  as  a  whole  do 
not  complete  the  idea,  unless  in  the  notion  of  the 
whole  you  include  the  relations  and  respects 
which  these  parts  have  to  each  other.  Every 
work,  both  of  nature  and  of  art,  is  a  system  ;  and 
as  every  particular  thing,  both  natural  and  artifi- 
cial, is  for  some  use  or  purpose  out  of  and  beyond 
itself,  one  may  add  to  what  has  been  already 
brought  into  the  idea  of  a  system,  its  conducive- 
ness  to  this  one  or  more  ends.  Let  us  instance 
in  a  watch — suppose  the  several  parts  of  it  taken 
to  pieces,  and  placed  apart  from  each  other  ;  let 
a  man  have  ever  so  exact  a  notion  of  these  several 
parts,  unless  he  considers  the  respects  and  relations 
which  they  have  to  each  other,  he  will  not  have 
anything  like  the  idea  of  a  watch.  Suppose  these 
several  parts  brought  together  and  anyhow  united  : 
neither  will  he  yet,  be  the  union  ever  so  close, 
have  an  idea  which  will  bear  any  resemblance  to 
that  of  a  watch.  But  let  him  view  these  several 
parts  put  together,  or  consider  them  as  to  be  put 
together  in  the  manner  of  a  watch  ;  let  him  form 
a  notion  of  the  relations  which  these  several  parts 
have  to  each  other — all  conducive  in  their  re- 
spective ways  to  this  purpose,  showing  the  hour 
of  the  day  ;  and  then  he  has  the  idea  of  a  watch. 
Thus  it  is  with  regard  to  the  inward  frame  of 


£66  QUOTATIONS   OK   SYSTEM. 

man.  Appetites,  passions,  affections,  and  the 
principle  of  reflection,  considered  merely  as  the 
several  parts  of  our  inward  nature,  do  not  give  us 
an  idea  of  the  system  or  constitution  of  this 
nature  ;  because  the  constitution  is  formed  by 
somewhat  not  yet  taken  into  consideration, 
namely,  by  the  relations  which  these  several 
parts  have  to  each  other,  the  chief  of  which  is 
the  authority  of  reflection  or  conscience.  It  is 
from  considering  the  relations  which  the  several 
appetites  and  passions  in  the  inward  frame  have 
to  each  other,  and,  above  all,  the  supremacy  of 
reflection  or  conscience,  that  we  get  the  idea  of 
the  system  or  constitution  of  human  nature. 
And  from  the  idea  itself  it  will  as  fully  appear, 
that  this  our  nature,  i.e.,  constitution,  is  adapted 
to  virtue,  as  from  the  idea  of  a  watch  it  appears 
that  its  nature,  i.e.,  constitution  or  system,  is 
adapted  to  measure  time." 


QUOTATIONS  ON  ANALYSIS. 

APPENDIX    C. 

227.  From  Fleming's  Vocabulary  of  Philos- 
ophy, ed.  1867. 

ANALYSIS  and  SYNTHESIS,  or  decomposition  and 
recomposition.  Objects  of  sense  and  of  thought 
are  presented  to  us  in  a  complex  state,  but  we  can 
only,  or  at  least  best,  understand  what  is  simple. 
Among  the  varied  objects  of  a  landscape,  I  be- 
hold a  tree,  I  separate  it  from  the  other  objects, 
I  examine  separately  its  different  parts — trunk, 
branches,  leaves,  etc.,  and  then  reuniting  them 
into  one  whole  I  form  a  notion  of  the  tree.  The 
first  part  of  this  process  is  analysis,  the  second 
is  synthesis.  If  this  must  be  done  with  an  indi- 
vidual, it  is  more  necessary  with  the  infinitude 
of  objects  which  surround  us,  to  evolve  the  one 
out  of  many,  to  recall  the  multitude  to  unity. 
We  compare  objects  with  one  another  to  see 
wherein  they  agree  ;  we  next,  by  a  synthetical 
process,  infer  a  general  law,  or  generalize  the  co- 
incident qualities,  and  perform  an  act  of  induction 
which  is  purely  a  synthetical  process,  though 
commonly  called  analytical.  Thus,  from  our  ex- 
perience that  bodies  attract  within  certain  limits, 
we  infer  that  all  bodies  gravitate  towards  each 
other.  The  antecedent  here  only  says  that  cer- 


268  QUOTATIONS   OK   ANALYSIS. 

tain  bodies  gravitate,  the  consequent  says  all  bod- 
ies gravitate.  They  are  brought  together  by  the 
mental  insertion  of  a  third  proposition,  which  is, 
* i  that  nature  is  uniform. ' '  This  is  not  the 
product  of  induction,  but  antecedent  to  all  in- 
duction. The  statement  fully  expressed  is,  this 
and  that  body,  which  we  know,  gravitate,  but 
nature  is  uniform  ;  this  and  that  body  repre- 
sent all  bodies — all  bodies  gravitate.  It  is  the 
mind  which  connects  these  things,  and  the  pro- 
cess is  synthetical.  This  is  the  one  universal 
method  in  all  philosophy,  and  different  schools 
have  differed  only  in  the  way  of  employing  it. 
Method  is  the  following  of  one  thing  through 
another.  Order  is  the  following  of  one  thing 
after  another.  Analysis  is  real,  as  when  a 
chemist  separates  two  substances.  Logical,  as 
when  we  consider  the  properties  of  the  sides  and 
angles  of  a  triangle  separately,  though  we  can- 
not think  of  a  triangle  without  sides  and  angles. 

The  instruments  of  analysis  are  observation 
and  experiment;  of  synthesis,  definition  and 
classification. 

Take  down  a  watch,  analysis  ;  put  it  up,  syn- 
thesis. 

Analysis  is  decomposing  what  is  compound  to 
detect  its  elements.  Objects  may  be  compound, 
as  consisting  of  several  distinct  parts  united,  or 
of  several  properties  equally  distinct.  In  the 
former  view,  analysis  will  divide  the  object  into 
its  parts,  and  present  them  to  us  successively,  and 
then  the  relations  by  which  they  are  united.  In 
the  second  case,  analysis  will  separate  the  dis- 


QUOTATION'S   ON   ANALYSIS.  269 

tinct  properties,  and  show  the  relations  of  every 
kind  which  may  be  between  them. 

Analysis  is  the  resolving  into  its  constituent 
elements  of  a  compound  heterogeneous  substance. 
Thus,  water  can  be  analyzed  into  oxygen  and  hy- 
drogen, atmospheric  air  into  these  and  azote. 

Abstraction  is  analysis,  since  it  is  decomposi- 
tion, but  what  distinguishes  it  is  that  it  is  exer- 
cised upon  qualities  which  by  themselves  have 
no  real  existence.  Classification  is  synthesis. 
Induction  rests  upon  analysis.  Deduction  is 
a  synthetical  process.  Demonstration  includes 
both. 


QUOTATIONS  ON  SYNTHESIS. 

APPENDIX    D. 

228.  From  Fleming's  Vocabulary  of  Phi- 
losophy, ed.  1867. 

SYNTHESIS  "  consists  in  assuming  the  causes 
discovered  and  established  as  principles,  and  by 
them  explaining  the  phenomena  proceeding  from 
them  and  proving  the  explanation. ' ' 

"  Every  synthesis  which  has  not  started  with 
a  complete  analysis  ends  at  a  result  which,  in 
Greek,  is  called  hypothesis  ;  instead  of  which,  if 
synthesis  has  been  preceded  by  a  sufficient 
analysis,  the  synthesis  founded  upon  that  anal- 
ysis leads  to  a  result  which  in  Greek  is  called 
system.  The  legitimacy  of  every  synthesis  is 
directly  owing  to  the  exactness  of  analysis; 
every  system  which  is  merely  an  hypothesis  is  a 
vain  system  ;  every  synthesis  which  has  not  been 
preceded  by  analysis  is  a  pure  imagination  :  but 
at  the  same  time  every  analysis  which  does  not 
aspire  to  a  synthesis  which  may  be  equal  to  it, 
is  an  analysis  which  halts  on  the  way.  On  the 
one  hand,  synthesis  without  analysis  gives  a  false 
science  ;  on  the  other  hand,  analysis  without 
synthesis  gives  an  incomplete  science.  An  in- 
complete science  is  a  hundred  times  more  valu- 


QUOTATIONS   ON   SYNTHESIS.  271 

able  than  a  false  science  ;  but  neither  a  false 
science  nor  an  incomplete  science  is  the  ideal  of 
science.  The  ideal  of  science,  the  ideal  of  phi- 
losophy, can  be  realized  only  by  a  method  which 
combines  the  two  processes  of  analysis  and 
synthesis, " 


QUOTATIONS   ON  DEFINITION. 

APPENDIX    E. 

229.  From  Fleming's  Vocabulary  of  Philos- 
ophy, ed.  1867. 

DEFINITION  (definio,  to  mark  out  limits). 

"  The  simplest  and  most  correct  notion  of  a 
definition  is,  a  proposition  declaratory  of  the 
meaning  of  a  word. ' ' 

Definition  signifies  "  laying  down  a  bound- 
ary ;"  and  is  used  in  Logic  to  signify  "  an  ex- 
pression which  explains  any  term  so  as  to  sepa- 
rate it  from  everything  else,  as  a  boundary  sep- 
arates fields.  Logicians  distinguish  definitions 
into  Nominal  and  Real. 

"  Definitions  are  called  nominal,  which  ex- 
plain merely  the  meaning  of  the  term ;  and  real, 
which  explain  the  nature  of  the  thing  signified 
by  that  term.  Logic  is  concerned  with  nominal 
definitions  alone.  ' ' 

"  By  a  real,  in  contrast  to  a  verbal  or  nomi- 
nal definition,  the  logicians  do  not  intend  i  the 
giving  an  adequate  conception  of  the  nature  and 
essence  of  a  thing  ;'  that  is,  of  a  thing  considered 
in  itself,  and  apart  from  the  conceptions  of  it 
already  possessed.  By  verbal  definition  is  meant 
the  more  accurate  determination  of  the  significa- 


QUOTATIONS   ON   DEFINITION.  273 

tion  of  a  word ;  by  real  the  more  accurate  deter- 
mination of  the  contents  of  a  notion.  The  one 
clears  up  the  relation  of  words  to  notions ;  the 
other  of  notions  to  things.  The  substitution  of 
notional  for  real  would,  perhaps,  remove  the 
ambiguity.  But  if  we  retain  the  term  real,  the 
aim  of  a  verbal  definition  being  to  specify  the 
thought  denoted  by  the  word,  such  definition 
ought  to  be  called  notional,  on  the  principle  on 
which  the  definition  of  a  notion  is  called  real ; 
for  this  definition  is  the  exposition  of  what  things 
are  comprehended  in  a  thought. ' ' 

"  In  the  sense  in  which  nominal  and  real 
definitions  were  distinguished  by  the  scholastic 
logicians,  logic  is  concerned  with  real,  i.e., 
notional  definitions  only  ;  to  explain  the  mean- 
ing of  words  belongs  to  dictionaries  or  gram- 
mars. ' ' 

i 1  There  is  a  real  distinction  between  definitions 
of  names  and  what  are  erroneously  called  defini- 
tions of  things  ;  but  it  is  that  the  latter,  along 
with  the  meaning  of  a  name,  covertly  asserts  a 
matter  of  fact.  This  covert  assertion  is  not  a 
definition,  but  a  postulate.  The  definition  is  a 
mere  identical  proposition,  which  gives  informa- 
tion only  about  the  use  of  language,  and  from 
which  no  conclusions  respecting  matters  of  fact 
can  possibly  be  drawn.  The  accompanying  pos- 
tulate, on  the  other  hand,  affirms  a  fact  which 
may  lead  to  consequences  of  every  degree  of  im- 
portance. It  affirms  the  real  existence  of  things, 
possessing  the  combination  of  attributes  set  forth 
in  the  definition,  and  this,  if  true,  may  be  foun- 


274  QUOTATIONS   ON    DEFINITION. 

dation  sufficient  to  build  a  whole  fabric  of  scien- 
tific truth." 

Real  definitions  are  divided  into  essential  and 
accidental.  An  essential  definition  states  what 
are  regarded  as  the  constituent  parts  of  the  es- 
sence of  that  which  is  to  be  defined  ;  and  an  ac- 
cidental definition  (or  description)  lays  down 
what  are  regarded  as  circumstances  belonging  to 
it,  viz.,  properties  or  accidents,  such  as  causes, 
effects,  &c. 

"  Essential  definition  is  divided  into  physical 
(natural)  and  logical  (metaphysical)  ;  the  phy- 
sical definition  being  made  by  an  enumeration  of 
such  parts  as  are  actually  separable  ;  such  as  are 
the  hull,  masts,  &c. ,  of  a  i  ship  '  ;  the  root,  trunk, 
branches,  bark,  &c.,  of  a  'tree.'  The  logical 
definition  consists  of  the  genus  and  difference, 
which  are  called  by  some  the  metaphysical 
(ideal)  parts  ;  as  being  not  two  real  parts  into 
which  an  individual  object  can  (as  in  the  former 
case),  be  actually  divided,  but  only  different 
views  taken  (notions  formed)  of  a  class  of  objects, 
by  one  mind.  Thus  a  magnet  would  be  defined 
logically,  '  an  iron  ore  having  attraction  for 
iron/  " 

Accidental  or  descriptive  definition  may  be — 
1 .  Causal ;  as  when  man  is  defined  as  made 
after  the  image  of  God,  and  for  his  glory.  2. 
Accidental ;  as  when  he  is  defined  to  be  ani- 
mal, bipes  implume.  3.  Genetic;  as  when  the 
means  by  which  it  is  made  are  indicated  ;  as,  if  a 
straight  line  fixed  at  one  end  be  drawn  round  by 
the  other  end  so  as  to  return  to  itself,  a  circle 


QUOTATIONS   ON    DEFINITION.  275 

will  be  described.  Or,  4.  Per  opposition ;  as, 
when  virtue  is  said  to  be  flying  from  vice. 

The  rules  of  a  good  definition  are  : — 1.  That  it 
be  adequate.  If  .it  be  too  narrow,  you  explain 
a  part  instead  of  a  whole ;  if  too  extensive,  a 
whole  instead  of  a  part.  2.  That  it  be  clearer 
(i.e.,  consist  of  ideas  less  complex)  than  the 
thing  defined.  3.  That  it  be  in  just  a  sufficient 
number  of  proper  words.  Metaphorical  words 
are  excluded  because  they  are  indefinite. 

2.  From  Mill's  System  of  Logic,  pp.  105-106, 
8°  edition. 

The  simplest  and  most  correct  notion  of  a 
Definition  is,  a  proposition  declaratory  of  the 
meaning  of  a  word  ;  namely,  either  the  meaning 
which  it  bears  in  common  acceptation,  or  that 
which  the  speaker  or  writer,  for  the  particular 
purposes  of  his  discourse,  intends  to  annex  to  it. 
....  This  form  of  definition  is  the  most  pre- 
cise and  least  equivocal  of  any  ;  but  it  is  not 
brief  enough,  and  is  besides  too  technical  for 
common  discourse.  The  more  usual  mode  of  de- 
claring the  connotation  of  a  name,  is  to  predicate 
of  it  another  name  or  names  of  known  significa- 
tion, which  connote  the  same  aggregation  of  at- 
tributes  The  definition  of  a  name,  ac- 
cording to  this  view  of  it,  is  the  sum  total  of  all 
the  essential  propositions  which  can  be  framed 
with  that  name  for  their  subject.  All  proposi- 
tions the  truth  of  which  is  implied  in  the  name, 
all  those  which  we  are  made  aware  of  by  merely 
hearing  the  name,  are  included  in  the  definition, 
if  complete,  and  may  be  evolved  from  it  without 


276  QUOTATIONS   ON    DEFINITION. 

the  aid  of  any  other  premises  ;  whether  the  defi- 
nition expresses  them  in  two  or  three  words,  or 
in  a  larger  number.  It  is,  therefore,  not  with- 
out reason  that  Condillac  and  other  writers  have 
affirmed  a  definition  to  be  an  analysis.  To  re- 
solve any  complex  whole  into  the  elements  of 
which  it  is  compounded,  is  the  meaning  of  anal- 
ysis :  and  this  we  do  when  we  replace  one  word 
which  connotes  a  set  of  attributes  collectively,  by 
two  or  more  which  connote  the  same  attributes 
singly,  or  in  smaller  groups. 


QUOTATIONS  ON  ABSTRACTION. 

APPENDIX    F. 

230.  From  Fleming's  Vocabulary  of  Philos- 
ophy. 

ABSTRACT,  ABSTRACTION  (abstractio,  from 
abs  traho,  to  draw  away  from.  It  is  also  called 
separatio  and  resolutio) .  Dobrisch  observes  that 
the  term  abstraction  is  used  sometimes  in  a  psy- 
chological, sometimes  in  a  logical  sense.  In  the 
former  we  are  said  to  abstract  the  attention  from 
certain  distinctive  features  of  objects  presented. 
In  the  latter,  we  are  said  to  abstract  certain  por- 
tions of  a  given  concept  from  the  remainder. 
(Mansel.) 

1  '  ABSTRACTION  (Psychological)/'  says  Mr. 
Stewart,  "  is  the  power  of  considering  certain 
qualities  or  attributes  of  an  object  apart  from  the 
rest  ;  or,  as  I  would  rather  choose  to  define  it, 
the  power  which  the  understanding  has  of  sepa- 
rating the  combinations  which  are  presented  to 
it."  Perhaps  it  may  be  more  correctly  regarded 
as  a  process  rather  than  a  power — as  a  function 
rather  than  a  faculty.  Dr.  Reid  has  called  it  ' i  an 
operation  of  the  understanding. "  .  .  .  The 
chemist  separates  into  their  elements  those  bodies, 
which  are  submitted  to  his  analysis.  The  psy- 


278         QUOTATIONS   ON   ABSTRACTION. 

chologist  does  the  same  thing  mentally.  ...  In 
contemplating  mind,  he  may  think  of  its  capacity 
of  feeling  without  thinking  of  its  power  of  activ- 
ity, or  the  faculty  of  memory  apart  from  any  or 
all  of  the  other  faculties  with  which  it  is  al- 
lied. 

ABSTRACTION  (LOGICAL),  "  As  we  have  de- 
scribed it,"  says  Mr.  Thomson  (Outline  of  the 
Laws  of  Thought  p.  107),  "  would  include  three 
separate  acts  ;  first,  an  act  of  comparison,  which 
brings  several  intuitions  together  ;  next,  one  of 
reflection,  which  seeks  for  some  marks  which 
they  all  possess,  and  by  which  they  may  be  com- 
bined into  one  group  ;  and  last,  one  of  general- 
ization, which  forms  the  new  general  notion  or 
conception.  Kant,  however,  confines  the  name 
of  abstraction  to  the  last  of  the  three  ;  others 
apply  it  to  the  second.  It  is  not  of  much  conse- 
quence whether  we  enlarge  or  narrow  the  mean- 
ing of  the  word,  so  long  as  we  see  the  various 
steps  in  the  process.  The  word  means  a  draw- 
ing away  of  the  common  marks  from  all  the  dis- 
tinctive marks  which  the  single  objects  have. "  .  . 
Mr.  J.  S.  Mill  uses  the  term  abstract  as  opposed 
to  concrete.  By  an  abstract  name  he  means  the 
name  of  an  attribute — by  a  concrete  name  the 
name  of  an  object. 


QUOTATIONS  ON  GENERALIZATION. 

APPENDIX    G. 

231.  1.  From  Fleming's  Vocabulary  of  Phi- 
losophy, ed.  1867. 

Generalization  '  *  is  the  act  of  comprehending, 
under  a  common  name,  several  objects  agreeing" 
in  some  point  which  we  abstract  from  each  of 
them,  and  which  that  common  name  serves  to  in- 
dicate." 

"  When  we  are  contemplating  several  individ- 
uals which  resemble  each  other  in  some  part  of 
their  nature,  we  can  (by  attending  to  that  part 
alone,  and  not  to  those  points  wherein  they 
differ)  assign  them  one  common  name,  which  will 
express  or  stand  for  them  merely  as  far  as  they 
all  agree ;  and  which,  of  course,  will  be  appli- 
cable to  all  or  any  of  them  (which  process  is 
called  generalization)  ;  and  each  of  these  names 
is  called  a  common  term,  from  its  belonging  to 
them  all  alike ;  or  a  predicable,  because  it  may 
be  predicated  affirmatively  of  them  or  any  of 
them." 

Generalization  is  of  two  kinds — classification 
and  generalization  properly  so  called. 

When  we  observe  facts  accompanied  by  di- 
verse circumstances,  and  reduce  these  circum- 


280     QUOTATIONS   ON   GENERALIZATION. 

stances  to  such  as  are  essential  and  common,  we 
obtain  a  law. 

When  we  observe  individual  objects  and  ar- 
range them  according  to  their  common  charac 
ters,  we  obtain  a  class.  When  the  characters 
selected  are  such  as  belong  essentially  to  the  na- 
ture of  the  objects,  the  class  corresponds  with 
the  law.  When  the  character  selected  is  not 
natural  the  classification  is  artificial.  If  we  were 
to  class  animals  into  white  and  red,  we  would 
have  a  classification  which  had  no  reference  to 
the  laws  of  their  nature.  But  if  we  classify  them 
as  vertebrate  or  invertebrate,  we  have  a  classi- 
fication founded  on  their  organization.  Artificial 
classification  is  of  no  value  in  science,  it  is  a 
mere  aid  to  the  memory.  Natural  classification 
is  the  foundation  of  all  science.  This  is  some- 
times called  generalization.  It  is  more  properly 
classification. 

The  law  of  gravitation  is  exemplified  in  the  fall 
of  a  single  stone  to  the  ground.  But  many  stones 
and  other  heavy  bodies  must  have  been  observed 
to  fall  before  the  fact  was  generalized,  and  the 
law  stated.  And  in  this  process  of  generalizing 
there  is  involved  a  principle  which  experience 
does  not  furnish.  Experience,  how  extensive 
soever  it  may  be,  can  only  give  the  particular,  yet 
from  the  particular  we  rise  to  the  general,  and 
affirm  not  only  that  all  heavy  bodies  which  have 
been  observed,  but  that  all  heavy  bodies  whether 
they  have  been  observed  or  not,  gravitate.  In 
this  is  implied  a  belief  that  there  is  order  in  na- 
ture, that  under  the  same  circumstances  the  same 


QUOTATIONS   ON   GENERALIZATION.      281 

substances  will  present  the  same  phenomena. 
This  is  a  principle  furnished  by  reason,  the  pro- 
cess founded  on  it  embodies  elements  furnished 
by  experience. 

The  results  of  generalization  are  general  no- 
tions expressed  by  general  terms.  Objects  are 
classed  according  to  certain  properties  which  they 
have  in  common,  into  genera  and  species. 
Hence  arose  the  question  which  caused  centuries 
of  acrimonious  discussion.  Have  genera  and 
species  a  real,  independent  existence,  or  are  they 
only  to  be  found  in  the  mind  ? 

The  principle  of  generalization  is,  that  be- 
ings howsoever  different  agree  or  are  homo- 
geneous in  some  respect. 

2.  From  Jevon's  Principles  of  Science,  pp. 
597-599,  ed.  1877. 

The  term  generalization,  as  commonly  used, 
includes  two  processes  which  are  of  different 
character,  but  are  often  closely  associated  to- 
gether. In  the  first  place,  we  generalize  when 
we  .recognize  even  in  two  objects  a  common  na- 
ture. We  cannot  detect  the  slightest  similarity 
without  opening  the  way  to  inference  from  one 
case  to  the  other.  If  we  compare  a  cubical  crys- 
tal with  a  regular  octahedron,  there  is  little  ap- 
parent similarity  ;  but,  as  soon  as  we  perceive  that 
either  can  be  produced  by  the  symmetrical  modi- 
fication of  the  other,  we  discover  a  groundwork  of 
similarity  in  the  crystals,  which  enable  us  to  infer 
many  things  of  one,  because  they  are  true  of  the 
other.  Our  knowledge  of  ozone  took  its  rise 
from  the  time  when  the  similarity  of  smell,  at- 


282     QUOTATIONS   ON   GENERALIZATION. 

tending  electric  sparks,  strokes  of  lightning,  and 
the  slow  combustion  of  phosphorus,  was  noticed 
by  Schonbein.  There  was  a  time  when  the  rain- 
bow was  an  inexplicable  phenomenon — a  portent, 
like  a  comet,  and  a  cause  of  superstitious  hopes 
and  fears.  But  we  find  the  true  spirit  of  science 
in  Roger  Bacon,  who  desires  us  to  consider  the 
objects  which  present  the  same  colours  as  the  rain- 
bow ;  he  mentions  hexagonal  crystals  from  Ire- 
land and  India,  but  he  bids  us  not  suppose  that 
the  hexagonal  form  is  essential,  for  similar  colours 
may  be  detected  in  many  transparent  stones. 
Drops  of  water  scattered  by  the  oar  in  the  sun, 
the  spray  from  a  water-wheel,  the  dewdrops  lying 
on  the  grass  in  the  summer  morning,  all  display 
a  similar  phenomenon.  No  sooner  have  we 
grouped  together  these  apparently  diverse  in- 
stances, than  we  have  begun  to  generalise,  and 
have  acquired  a  power  of  applying  to  one  in- 
stance what  we  can  detect  of  others.  Even  when 
we  do  not  apply  the  knowledge  gained  to  new 
objects,  our  comprehension  of  those  already  ob- 
served is  greatly  strengthened  and  deepened  by 
learning  to  view  them  as  particular  cases  of  a 
more  general  property. 

A  second  process,  to  which  the  name  of  gen- 
eralization is  often  given,  consists  in  passing  from 
a  fact  or  partial  law  to  a  multitude  of  unexamined 
cases,  which  we  believe  to  be  subject  to  the  same 
conditions.  Instead  of  merely  recognising  sim- 
ilarity as  it  is  brought  before  us,  we  predict  its 
existence  before  our  senses  can  detect  it,  so  that 
generalisation  of  this  kind  endows  us  with  a 


QUOTATIONS   ON   GENERALIZATION.      283 

prophetic  power  of  more  or  less  probability. 
Having  observed  that  many  substances  assume, 
like  water  and  mercury,  the  three  states  of  solid, 
liquid,  and  gas,  and  having  assured  ourselves  by 
frequent  trial  that  the  greater  the  means  we 
possess  of  heating  and  cooling,  the  more  sub- 
stances we  can  vaporise  and  freeze,  we  pass  con- 
fidently in  advance  of  fact,  and  assume  that  all 
substances  are  capable  of  these  three  forms. 
Such  a  generalisation  was  accepted  by  Lavoisier 
and  Laplace  before  many  of  the  corroborative 
facts  now  in  our  possession  were  known.  The 
reduction  of  a  single  comet  beneath  the  sway  of 
gravity  was  considered  sufficient  indication  that 
all  comets  obey  the  same  power.  Few  persons 
doubted  that  the  law  of  gravity  extended  over 
the  whole  heavens  ;  certainly  the  fact  that  a  few 
stars  out  of  many  millions  manifest  the  action  of 
gravity,  is  now  held  to  be  sufficient  evidence  of 
its  general  extension  over  the  visible  universe 


QUOTATIONS    ON    CLASSIFICATION. 

APPENDIX    H. 

232.  1.  From  Fleming's  Vocabulary  of  Phi  - 
losophy,  ed.  1858,  pp.  91-92. 

"  Montesquieu  observed  very  justly,  that  in 
their  classification  of  the  citizens,  the  great 
legislators  of  antiquity  made  the  greatest  display 
of  their  powers,  and  even  soared  above  them- 
selves. ' '  Burke,  On  the  French  Revolution. 

"  A  class  consists  of  several  things  coming 
under  a  common  description. ' '  Whately,  Log. , 
b.  i.,  §  3. 

"  The  sorting  of  a  multitude  of  things  into 
parcels,  for  the  sake  of  knowing  them  better, 
and  remembering  them  more  easily,  is  classifica- 
tion. When  we  attempt  to  classify  a  multitude 
of  things,  we  first  observe  some  respects  in 
which  they  differ  from  each  other  ;  for  we  could 
not  classify  things  that  are  entirely  alike  ;  as, 
for  instance,  a  bushel  of  peas  ;  we  then  separate 
things  that  are  not  alike,  and  bring  together 
things  that  are  similar."  Taylor,  Elements  of 
Thought. 

"  In  every  act  of  classification,  two  steps  must 
be  taken  ;  certain  marks  are  to  be  selected,  the 
possession  of  which  is  to  be  the  title  to  admis- 


QUOTATIONS   OK   CLASSIFICATION.      285 

sion  into  the  class,  and  then  all  the  objects  that 
possess  them  are  to  be  ascertained.  When  the 
marks  selected  are  really  important  and  con- 
nected closely  with  the  nature  and  functions  of 
the  thing,  the  classification  is  said  to  be  natu- 
ral ;  where  they  are  such  as  do  not  affect  the 
nature  of  the  objects  materially,  and  belong  in 
common  to  things  the  most  different  in  their 
main  properties,  it  is  artificial."  Thomson, 
Outline  of  Laws  of  Thought,  2d  edit.,  p.  377. 

The  condition  common  to  both  modes  of  clas- 
sification, is  to  comprehend  everything  and  to 
suppose  nothing.  But  the  rules  for  a  natural 
classification  are  more  strict  than  for  an  artificial 
or  arbitrary  one.  We  may  classify  objects  arbi- 
trarily in  any  point  of  view  in  which  we  are 
pleased  to  regard  them.  But  a  natural  classifi- 
cation can  only  proceed  according  to  the  real 
nature  and  qualities  of  the  objects.  The  advan- 
tages of  classification  are  to  give  a  convenient 
form  to  our  acquirements,  and  to  enlarge  our 
knowledge  of  the  relations  in  which  different  ob- 
jects stand  to  one  another.  A  good  classifica- 
tion should — 1st,  Rest  on  one  principle  or  analo- 
gous principles.  2d,  The  principle  or  princi- 
ples should  be  of  a  constant  and  permanent  char- 
acter. 3d,  It  should  be  natural,  that  is,  even 
when  artificial,  it  should  not  be  violent  or 
forced.  4th,  It  should  clearly  and  easily  apply 
to  all  the  objects  classified. 

The  principles  on  which  classification  rests 
are  these: — 1st,  of  Generalization;  2d,  of 
Specification ;  and  3d,  of  Continuity. 


286      QUOTATIONS   ON   CLASSIFICATION. 

Classification  proceeds  upon  observed  resem- 
blances. Generalization  rests  upon  the  princi- 
ple, that  the  same  or  similar  causes  will  produce 
similar  effects. — Mill,  Log.,  b.  i.,  chap.  7,  §  4  ; 
McCosh,  Typical  Forms,  b.  iii.,  chap.  1. 

2.  From  Jevons'  Elementary  Lessons  in  Logic, 
ed.  1878,  pp.  276-286. 

It  may  be  said  that  the  subject  we  are  treating 
is  coextensive  with  the  science  of  logic.  All 
thought,  all  reasoning,  so  far  as  it  deals  with 
general  names  or  general  notions,  may  be  said 
to  consist  in  classification.  Every  common 
name  or  general  name  is  the  name  of  a  class,  and 
every  name  of  a  class  is  a  common  name. 
"  Metal  "  is  the  name  of  one  class  of  substantives 
so  often  used  in  our  syllogistic  examples  ; 
* '  Element' '  of  another  class,  of  which  the  former 
class  is  part.  Reasoning  has  been  plausibly  rep- 
resented to  consist  in  affirming  of  the  parts  of  a 
class  whatever  may  be  affirmed  of  the  whole. 
Every  law  of  nature  which  we  arrive  at  enables 
us  to  classify  together  a  number  of  facts,  and  it 
would  hardly  be  too  much  to  define  logic  as  the 
theory  of  classification.  .  .  .  Classification 
may  perhaps  be  best  defined  as  the  arrange- 
ment of  things,  or  our  notions  of  them,  accord- 
ing to  their  resemblances,  or  identities. 

Every  class  should  so  be  constituted  as  to  con- 
tain objects  exactly  resembling  each  other  in 
certain  definite  qualities,  which  are  stated  in  the 
definition  of  the  class.  The  more  numerous  and 
extensive  the  resemblances  which  are  thus  indi- 


QUOTATIONS   ON   CLASSIFICATION.      28? 

cated  by  any  system  of  classes,  the  more  perfect 
and  useful  must  that  system  be  considered. 

Mr.  Mill  thus  describes  his  view  of  the  mean- 
ing— i '  Classification  is  a  contrivance  for  the  best 
possible  ordering  of  the  ideas  of  objects  in  our 
minds  ;  for  causing  the  ideas  to  accompany  or 
succeed  one  another  in  such  a  way  as  shall  give 
us  the  greatest  command  over  our  knowledge 
already  acquired,  and  lead  most  directly  to  the 
acquisition  of  more.  The  general  problem  of 
classification,  in  reference  to  these  purposes  may 
be  stated  as  follows  :  To  provide  that  things  shall 
be  thought  of  in  such  groups,  and  those  groups 
in  such  an  order,  as  will  best  conduce  to  the  re- 
membrance, and  to  the  ascertainment  .of  their 
laws." 

A  collection  of  objects  may  be  classified  in  an 
indefinite  number  of  ways.  Any  quality  which 
is  possessed  by  some  and  not  by  others  may  be 
taken  as  the  first  difference,  and  the  groups  thus 
distinguished  may  be  subdivided  in  succession  by 
any  other  qualities  taken  at  will.  Thus  a  library 
of  books  might  be  arranged,  (1)  according  to 
size,  (2)  according  to  the  language  in  which 
they  are  written,  (3)  according  to  the  alphabetic 
order  of  their  authors'  names,  (4)  according 
to  their  subjects  ;  and  in  various  other  ways. 
In  large  libraries  and  in  catalogues  such  modes 
of  arrangement  are  adopted  and  variously  com- 
bined. .  .  .  The  population  of  a  kingdom,  again, 
may  be  classified  in  an  almost  endless  number  of 
ways  with  regard  to  different  purposes  or  sci- 
ences. The  population  of  the  United  Kingdom 


288    QUOTATIONS  ON  CLASSIFICATION. 

may  be  divided  according  to  their  place  of  birth, 
as  English,  Welsh,  Scotch,  Irish,  Colonial -born 
and  aliens.  The  ethnographer  would  divide 
them  into  Anglo-Saxons,  Cymri,  Gaels,  Picts, 
&c.  The  statist  arranges  them  according  to  age  ; 
to  condition,  as  married,  unmarried,  widowed, 
etc.  ;  to  state  of  body,  as  able,  incapacitated, 
blind,  imbecile.  .  .  . 

In  the  natural  world,  again,  we  may  mak^  va- 
rious classifications.  Plants  may  be  arranged 
according  to  the  country  from  which  they  are 
derived  ;  the  kind  of  place  or  habitat  in  which 
they  flourish  ;  the  time  they  live,  as  annual, 
biennial,  perennial  ;  their  size,  as  herbs,  shrubs, 
trees  ;  their  properties,  as  esculents,  drugs,  or 
poisons  :  all  these  are  distinct  from  the  classifi- 
cations which  the  botanist  devises  to  represent 
the  natural  affinities  or  relationships  of  plants. 
It  is  thus  evident  that  in  making  a  classification 
we  have  no  one  fixed  method  which  can  be  ascer- 
tained by  rule,  but  that  an  indefinite  number  of 
choices  or  alternatives  are  usually  open  to  us. 
Logic  cannot  in  such  cases  do  much  ;  and  it  is 
really  the  work  of  the  special  sciences  to  investi- 
gate the  character  of  the  classification  required. 
All  that  logic  can  do  is  to  point  out  certain  gen- 
eral requirements  and  principles. 

The  first  requisite  of  a  good  classification  is, 
that  it  should  be  appropriate  to  the  purpose  in 
hand ;  that  is  to  say,  the  points  of  resemblance 
selected  to  form  the  leading  classes  shall  be  those 
of  importance  to  the  practical  use  of  the  classifi- 
cation. All  those  things  must  be  arranged  to- 


QUOTATIONS   ON   CLASSIFICATION.      289 

gether  which  require  to  be  treated  alike,  and 
those  things  must  be  separated  which  require  to 
be  treated  separately.  ... 

Another  and,  in  a  scientific  point  of  view, 
the  most  important  requisite  of  a  good  classifica- 
tion, is  that  it  shall  enable  the  greatest  possi- 
ble number  of  general  assertions  to  be  made. 
This  is  the  criterion,  as  stated  by  Dr.  Whewell, 
which  distinguishes  a  natural  from  an  artificial 
system  of  classification,  and  we  must  carefully 
dwell  upon  its  meaning.  It  will  be  apparent 
that  a  good  classification  is  more  than  a  mere 
orderly  arrangement  ;  it  involves  a  process  of 
induction  which  will  bring  to  light  all  the  more 
general  relations  which  exist  between  the  things 
classified.  An  arrangement  of  books  will  gen- 
erally be  artificial ;  the  octavo  volumes  will  not 
have  any  common  character  except  being  of  an 
octavo  size.  An  alphabetical  arrangement  of 
names  again  is  exceedingly  appropriate  and  con- 
venient to  many  purposes,  but  is  artificial  because 
it  allows  of  few  or  no  general  assertions.  We 
cannot  make  any  general  assertions  whatever 
about  persons  because  their  names  happen  to 
begin  with  an  A  or  a  B,  a  P  or  a  W. 

In  a  classification  of  plants  again  we  meet 
with  most  deep  and  natural  distinctions  between 
the  great  classes  called  Exogens,  Endogens,  and 
Acrogens.  .  .  .  These  are  the  very  widest 
classes  in  what  is  called  the  natural  system  of 
botanical  arrangement;  but  similar  principles 
are  observed  in  all  its  minor  classes. 

The  continual  efforts  of  botanists  are  directed 


290      QUOTATIONS   ON"   CLASSIFICATION. 

to  bringing  the  great  multitudes  of  plants  to- 
gether in  species,  genera,  orders,  classes,  and  in 
various  intermediate  groups,  so  that  the  members 
of  each  group  shall  have  the  greatest  number  of 
points  of  mutual  resemblance  and  the  fewest 
points  of  resemblance  to  members  of  other 
groups.  Thus  is  best  fulfilled  the  great  purpose 
of  classification,  which  reduces  multiplicity  to 
unity,  and  enables  us  to  infer  of  all  the  other 
members  of  a  class  what  we  know  of  any  one 
member,  provided  we  distinguish  properly  be- 
tween those  qualities  which  are  likely  or  are 
known  to  belong  to  the  class,  and  those  which 
are  peculiar  to  the  individual.  It  is  a  necessary 
condition  of  correct  classification,  as  remarked  by 
Prof.  Huxley,  that  the  definition  of  a  group 
shall  hold  exactly  true  of  all  the  members  of  a 
group,  and  not  of  the  members  of  any  other 
group.  .  .  . 

Natural  classifications  give  us  the  deepest  re- 
semblances and  relations,  and  may  lead  us  ulti- 
mately to  a  knowledge  of  the  way  in  which  the 
varieties  of  things  are  produced.  They  are, 
therefore,  essential  to  a  true  science,  and  may  al- 
most be  said  to  constitute  the  framework  of  the 
science.  .  .  . 

Closely  connected  with  the  process  of  Classifi- 
cation is  that  of  abstraction.  To  abstract  is  to 
separate  the  qualities  common  to  all  individuals 
-of  a  group  from  the  peculiarities  of  each  individ- 
ual. The  notion  "  triangle"  is  the  result  of  ab- 
straction in  so  far  as  we  can  reason  concerning 
triangles,  without  any  regard  to  the  particular 


QUOTATIONS   ON   CLASSIFICATION.       291 

size  or  shape  of  any  one  triangle.  All  classifica- 
tion implies  abstraction,  for  in  framing  and 
defining  the  class  I  must  separate  the  common 
qualities  from  the  peculiarities.  When  I  ab- 
stract, too,  I  form  a  general  conception,  or  one, 
which,  generally  speaking,  embraces  many  ob- 
jects. If,  indeed,  the  quality  abstracted  is  a  pe- 
culiar property  of  the  class,  or  one  which  belongs 
to  the  whole  and  not  to  any  other  objects,  I 
may  not  increase  the  extent  of  the  notion,  so  that 
Mr.  Herbert  Spencer  is,  perhaps,  right  in  holding 
that  we  can  abstract  without  generalizing. 
We  often  use  this  word  generalization,  and 
the  process  may  be  defined  as  inferring  of  a  whole 
class  what  we  know  only  of  a  part.  Whenever 
we  regard  the  qualities  of  a  thing  as  not  confined 
to  that  thing  only  but  as  extended  to  other  ob- 
jects ;  when,  in  fact,  we  consider  a  thing  only 
as  a  member  of  a  class,  we  are  said  to  generalize. 
.  .  .  Dr.  Whewell  added  to  the  superabundance 
of  terms  to  express  the  same  processes  when  he 
introduced  the  expression  Colligation  of  facts. 

Whenever  two  things  are  found  to  have  simi- 
lar properties  so  as  to  be  placed  in  the  same 
class  they  may  be  said  to  be  connected  to- 
gether. 

We  connect  together  the  places  of  a  planet  as 
it  moves  round  the  sun,  when  we  conceive  them 
as  points  upon  a  common  ellipse.  Whenever 
we  thus  join  together  previously  disconnected 
facts,  by  a  suitable  general  notion  or  hypothesis, 
we  are  said  to  colligate  them.  Dr.  Whewell 


292      QUOTATIONS   ON   CLASSIFICATION. 

adds  that  the  general  conceptions  employed  must 
be  (1)  clear,  and  (2)  appropriate  ;  but  it  may 
well  be  questioned  whether  there  is  anything 
really  different  in  these  processes  from  the  gen- 
eral process  of  natural  classification  which  we 
have  considered. 


QUOTATIONS  ON  INDUCTION. 

APPENDIX    I. 

233.  1.  From  Smith — Synonyms  Discrimi- 
nated— "  Inference" — ed.  1878. 

Inference  (Lat.  in,  and  ferre,  to  bring)  is  the 
broadest  of  these  terms  (see  below),  denoting  any 
process  by  which  from  one  truth  or  fact  laid  down 
or  known  we  draw  another.  Inference  may  be 
either  by  induction  or  deduction,  and  hence  may 
be  probable  or  certain.  Inference  by  induction 
is  more  or  less  probable,  except  where  all  cases 
of  the  kind  have  been  collated,  when  it  ceases, 
strictly  speaking,  to  be  inference,  and  is  only  the 
assigning  of  a  common  name,  or  stating  an  uni- 
versal proposition.  From  having  seen  twenty 
swans  all  white,  one  might  infer  that  all  swans 
are  so.  This  would  be  only  a  probability  in  it- 
self, and,  as  a  fact,  not  true.  In  induction  we 
observe  a  sufficient  number  of  individual  facts 
or  cases,  and  extending  by  analogy  what  is  true 
of  them  to  others  of  the  same  class,  establish  a 
general  principle  or  law.  This  is  the  method  of 
physical  science.  The  process  of  deduction  is 
the  converse  of  this.  We  lay  down  a  general 
truth,  and  connect  a  particular  case  with  it  by 
means  of  a  middle  term.  When  inference  is 


294  QUOTATIONS   OK   INDUCTION. 

conducted  by  the  syllogistic  process,  it  is  Deduc- 
tion (Lat.  deducere,  to  draw  from),  which,  if 
rightly  conducted,  must  be  logically  sound, 
though  not  necessarily  true  in  fact.  In  a  chain 
of  reasoning  the  minor,  subordinate,  or  less 
fully-expressed  conclusions  are  called  inferences, 
as  distinguished  from  the  great  common  infer- 
ence or  Conclusion,  which  terminates  and  estab- 
lishes, or,  as  it  were,  shuts  up  (Concludere,  to 
shut)  the  argument.  A  conclusion  is  a  proposi- 
tion viewed  relatively  to  others  from  which  it  has 
been  deduced.  A  Consequence  (Lat.  consequi, 
to  follow)  is  a  conclusion  regarded  as  admitting 
of  degrees  of  closeness  or  directness.  Between 
the  first  stage  of  any  argument  and  any  particu- 
lar consequence  several  links  of  reasoning  may 
intervene.  Hence  the  common  phrase,  * '  remote 
consequences,"  as  meaning  results  which  will 
follow  sooner  or  later  from  what  has  been  stated 
or  conceded. 

2.  From  Day's  Elements  of  Logic,  ed.  1868, 
p.  226. 

The  accepted  characteristics  of  Induction 
are  : 

(a)  It  is  a  process  of  Thought  that  is  identical 
in  essential  character  in  all  those  movements  of 
Intelligence  which  induce,  which  infer  mediately 
otherwise  than  by  deduction.  There  is  but  one 
Induction,  as  there  is  but  one  Deduction  in  all 
Thought. 

(6)  It  is  a  reasoning,  being  a  derivative  Judg- 
ment, not  a  Concept  ;  an  inference  from  a 
datum,  implying  a  new  proper  Judgment-Cog- 


QUOTATIONS  ON  INDUCTION.  295 

nition,  not  a  mere   synthesis  of  subjects  or  of 
predicates — that  is,  not  a  Concept. 

(c)  It  is  a  mediate  reasoning,  being  derived  not  * 
from  a  single  Judgment,  but  from  a  plurality  of 
Judgments,  related  to  each  other  under  the  rela- 
tionship of  part  to  complementary  part  in  two 
of  their  terms  which  are  alike  related  to  the 
third  or  middle  term  as  parts  to  a  whole. 

3.  From  Fleming's  Vocabulary  of  Philosophy, 
ed.  1858,  pp.  252-254. 

Method  or  Process  of  Induction. — "  It  has 
been  said  that  Aristotle  attributed  the  discovery 
of  induction  to  Socrates,  deriving  the  word 
from  the  Socratic  accumulation  of  instances, 
serving  as  antecedents  to  establish  the  requisite 
conclusion. " — Devey,  Log.,  p.  151,  note. 

Induction  is  a  kind  of  argument  which  infers, 
respecting  a  whole  class,  what  has  been  ascer- 
tained respecting  one  or  more  individuals  of  that 
class. — Whately,  Log.,  book  ii.,  chap.  5,  §  5. 

"Induction  is  that  operation  of  mind  by 
which  we  infer  that  what  we  know  to  be  true  in 
a  particular  case  or  cases,  will  be  true  in  all  cases 
which  resemble  the  former  in  certain  assignable 
respects.  In  other  words,  induction  is  the  pro- 
cess  by  which  we  conclude  that  what  is  true  of 
certain  individuals  of  a  class,  is  true  of  the  whole 
class,  or  that  what  is  true  at  certain  times  will  be 
true  under  similar  circumstances  at  all  times. " — 
Mill,  Log.,  b.  iii.,  ch.  2,  §  1. 

"  Induction  is  usually  denned  to  be  the  pro- 
cess of  drawing  a  general  rule  from  a  sufficient 
number  of  particular  cases  ;  deduction  is  the 


296  QUOTATIONS   OJS   INDUCTION. 

converse  process  of  proving  that  some  property 
belongs  to  the  particular  case  from  the  consider- 
ation that  it  belongs  to  the  whole  class  in  which 
the  case  is  found.  That  all  bodies  tend  to  fall 
towards  the  earth  is  a  truth  which  we  have  ob 
tained  from  examining  a  number  of  bodies  com- 
ing under  our  notice,  by  induction ;  if  from  this 
general  principle  we  argue  that  the  stone  we 
throw  from  our  hand  will  show  the  same  ten- 
dency, we  adopt  the  deductive  method.  .  .  . 
More  exactly,  we  may  define  the  inductive 
method  as  the  process  of  discovering  laws  and 
rules  from  facts,  and  causes  from  effects  ;  and 
the  deductive,  as  the  method  of  deriving  facts 
from  laws  and  effects  from  their  causes." — 
(Thomson,  Outline  of  the  Laws  of  Thought,  2d 
edit.,  pp.  321,  323.) 

According  to  Sir  William  Hamilton  (Discus- 
sions, p.  156),  "Induction  has  been  employed 
to  designate  three  very  different  operations — 1. 
The  objective  process  of  investigating  particular 
facts,  as  preparatory  to  induction,  which  is  not 
a  process  of  reasoning  of  any  kind.  2.  A  ma- 
terial illation  of  the  universal  from  the  singular, 
as  warranted  either  by  the  general  analogy  of 
nature,  or  the  special  presumptions  afforded  by 
the  object-matter  of  any  real  science.  3.  A  for- 
mal illation  of  the  universal  from  the  individual, 
as  legitimated  solely  by  the  laws  of  thought,  and 
abstract  from  the  conditions  of  this  or  that  '  par- 
ticular matter. '  The  second  of  these  is  the  in- 
ductive method  of  Bacon,  which  proceeds  by  way 
of  rejections  and  conclusions,  so  as  to  arrive  at 


QUOTATIONS   ON  INDUCTION.  297 

those  axioms  or  general  laws  from  which  we  infer 
by  way  of  synthesis  other  particulars  unknown 
to  us,  and  perhaps  placed  beyond  reach  of  direct 
examination.  Aristotle's  definition  coincides 
with  the  third,  and  *  induction  is  an  inference 
drawn  from  all  the  particulars  '  (Prior  Analyt., 
ii.,  c.  23).  The  second  and  third  have  been 
confounded.  But  the  second  is  not  a  logical  pro- 
cess at  all,  since  the  conclusion  is  not  necessarily 
inferrible  from  the  premiss,  for  the  some  of  the 
antecedent  does  not  necessarily  legitimate  the  all 
of  the  conclusion,  notwithstanding  that  the  pro- 
cedure may  be  warranted  by  the  material  problem 
of  the  science  or  the  fundamental  principles  of 
the  human  understanding.  The  third  alone  is 
properly  an  induction  of  Logic  ;  for  Logic  does 
not  consider  things,  but  the  general  forms  of 
thought  under  which  the  mind  conceives  them  ; 
and  the  logical  inference  is  not  determined  by 
any  relation  of  casuality  between  the  premiss 
and  the  conclusion,  but  by  the  subjective  relation 
of  reason  and  consequence  as  involved  in  the 
thought/' 

"  The  Baconian  or  Material  Induction  pro- 
ceeds on  the  assumption  of  general  laws  in  the 
relations  of  physical  phenomena,  and  endeavours, 
by  select  observations  and  experiments,  to  detect 
the  law  in  any  particular  case.  This,  whatever 
be  its  value  as  a  general  method  of  physical  in- 
vestigation, has  no  place  in  Formal  Logic.  The 
Aristotelian  or  Formal  Induction  proceeds  on 
the  assumption  of  general  laws  of  thought,  and 
inquires  into  the  instances  in  which,  by  such 


298  QUOTATIONS   ON   INDUCTION. 

laws,  we  are  necessitated  to  reason  from  an  accu- 
mulation of  particular  instances  to  an  universal 
rule." — Mansel,  Prolegom.  Log.,  p.  209. 

Principle  of  Induction. — By  the  principle  of 
induction  is  meant  the  ground  or  warrant  on 
which  we  conclude  that  what  has  happened  in 
certain  cases,  which  have  been  observed,  will  also 
happen  in  other  cases,  which  have  not  been  ob- 
served. This  principle  is  involved  in  the  words 
of  the  wise  man,  Eccles.  i.  9,  "  The  thing  that 
hath  been,  it  is  that  which  shall  be  :  and  that 
which  is  done  is  that  which  shall  be  done."  In 
nature  there  is  nothing  insulated.  All  things 
exist  in  consequence  of  a  sufficient  reason,  all 
events  occur  according  to  the  efficacy  of  proper 
causes.  In  the  language  of  Newton,  Effectuum 
naturalium  ejusdem  generis  esedem  sunt 
causae,  The  same  causes  produce  the  same 
effects.  The  principle  of  induction  is  an  appli- 
cation of  the  principle  of  casuality.  Phenomena 
have  their  proper  causes,  and  these  causes  ope- 
rate according  to  a  fixed  law.  This  law  has  been 
expressed  by  saying,  substance  is  persistent. 
Our  belief  in  the  established  order  of  nature  is  a 
primitive  judgment,  according  to  Dr.  Reid  and 
others,  and  the  ground  of  all  the  knowledge  we 
derive  from  experience.  According  to  others 
this  belief  is  a  result  or  inference  derived  from 
experience. 

4.  From  Whe well's  Novum  Organon  Reno- 
vaium,  3d  edition,  1858,  p.  139  : — 

The  Pure  Mathematical  Sciences  can  hardly 
be  called  Inductive  Sciences.  Their  principles 


QUOTATIONS   ON   INDUCTION.  299 

are  not  obtained  by  Induction  from  Facts,  but 
are  necessarily  assumed  in  reasoning  upon  the 
subject-matter  which  those  sciences  involve. 

5.   From  English   Cyclopaedia,  edition  1867. 

Induction  (srt&y&tyri),  as  defined  by  Arch- 
bishop Whately,  is  "  a  kind  of  argument  which 
infers  respecting  a  whole  class  what  has  been  as- 
certained respecting  one  or  more  individuals  of 
that  class. ' '  According  to  Sir  William  Hamilton 
the  word  has  been  employed  to  designate  three 
very  different  operations  : — 1 .  The  objective  pro- 
cess of  investigating  particular  facts,  as  prepara- 
tory to  Induction,  which  he  observes  is  manifestly 
not  a  process  of  reasoning  of  any  kind  ;  2.  A  ma- 
terial illation  of  a  universal  from  a  singular,  as 
warranted  either  by  the  general  analogy  of  na- 
ture or  the  special  presumptions  afforded  by  the 
object  matter  of  any  real  science  ;  3.  A  formal 
illation  of  a  universal  from  the  individual,  as 
legitimated  solely  by  the  laws  of  thought  and 
abstracted  from  the  conditions  of  any  particular 
matter.  The  second  of  these  operations  is  the 
inductive  method  of  Bacon,  which  proceeds  by 
means  of  rejections  and  conclusions,  so  as  to  ar- 
rive at  those  axioms  or  general  laws  from  which 
we  may  infer  by  way  of  synthesis  other  particu- 
lars unknown  to  us,  and  perhaps  placed  beyond 
reach  of  direct  examination.  ('  Nov.  Org.^ 
i  Aph.^  c.  iii.,  c.  v.)  Aristotle's  definition  co- 
incides with  the  third,  and  induction  i  i  is  an  in- 
ference drawn  from  all  particulars. ' '  (4  Prior 
Analy.J  ii.,  c.  xxiii.)  The  second  and  third 
processes  are  improperly  confounded  by  most 
writers  on  logic,  and  treated  as  one  simple  and 


300  QUOTATIONS   OK   INDUCTION. 

purely  logical  operation.  But  the  second  is  not 
a  logical  process  at  all  ;  since  the  conclusion  is 
not  necessarily  inferrible  from  the  premise,  for 
the  some  of  the  antecedent  does  not  necessarily 
legitimate  the  all  of  the  conclusion,  notwithstand- 
ing that  the  procedure  may  be  warranted  by  the 
material  problem  of  the  science,  or  the  funda- 
mental principles  of  the  human  understanding. 
The  third  alone  is  properly  an  induction  of  logic  ; 
for  logic  does  not  consider  things,  but  the  general 
forms  of  thought  under  which  the  mind  conceives 
them  ;  and  the  logical  inference  is  not  deter- 
mined by  any  relation  of  causality  between  the 
premise  and  conclusion,  but  by  the  subjective 
relation  of  reason  and  consequence  as  involved 
in  the  thought.  The  inductive  process  is  exactly 
the  reverse  of  the  deductive  ;  for  while  the  latter 
proceeds  from  the  whole  to  the  part,  the  former 
ascends  from  the  part  to  the  whole  :  since  it  is 
only  under  the  character  of  a  constituted  or  con- 
taining whole,  or  as  a  constituent  and  contained 
part,  that  anything  can  become  the  term  of  logi- 
cal argumentation.  Of  these  two  processes,  Sir 
William  Hamilton  gives  the  following  figures  : — 

Induction.  Deduction. 

XYZareA.  B  is  A. 

X  Y  Z  are  whole  B.  X  Y  Z  are  under  B. 

.  \  whole  B  is  A.  .  •.  X  Y  Z  are  A. 

or,  or, 

A  contains  X  Y  Z.  A  contains  B. 

X  Y  Z  contains  B.  B  contains  X  Y  Z. 

.*.    A  contains  B.  .*.    A  contains  X  Y  Z. 
This  confusion  of  material  and  logical  indue- 


QUOTATIONS   ON   INDUCTION.  301 

tion  led  Gillies  and  others  to  insist  on  the  same- 
ness of  the  Baconian  and  Aristotelian  induction  ; 
while  Campbell  and  Dugald  Stewart,  who  totally 
mistook  the  value  of  all  logical  inference,  yet 
rightly  maintained  their  difference. 

By  Aristotle,  induction  and  deduction  are 
viewed  as  in  certain  respects  similar  in  form  ; 
Lut  in  others  as  diametrically  opposed,  the  latter 
being  an  analysis  of  the  whole  into  its  parts,  by 
descending  from  the  more  general  to  the  more 
particular  ;  but  the  former  descends  by  a  syn- 
thetical process  from  the  parts  to  the  whole. 
The  logicians,  who  misapprehended  the  nature  of 
induction,  reduced  it  to  a  deductive  syllogism  of 
the  third  form,  and  thereby  overthrew  the  valid- 
ity of  all  deduction  itself,  since  the  latter  is  only 
possible  by  means  of  the  former,  which  legiti- 
mates the  proposition  from  which  its  reasoniifg 
proceeds. 

Again,  the  Aristotelian  induction  was  drawn 
from  all  the  particulars,  whereas  the  confusion 
which  Sir  W.  Hamilton  has  pointed  out  gave 
rise  to  a  division  of  the  inductive  process  into 
perfect  and  imperfect,  according  as  the  enumera- 
tion of  particulars  is  complete  or  incomplete. 
The  latter  gives  only  a  probable  result,  whereas 
the  necessity  of  the  conclusion  is  essential  to  all 
logical  inference,  as  its  demonstrative  stringency 
depends  upon  the  form  of  the  illation,  and  not 
upon  the  truth  of  the  premises.  It  is  proper  to 
add,  that  no  one  ever  knew  the  distinction  be- 
tween the  imperfect  and  perfect  forms  of  the 
•conclusion  better  than  Aristotle  himself. 


302  QUOTATIONS   ON   INDUCTION. 

Induction  (Mathematics).  The  method  of 
induction,  in  the  sense  in  which  the  word  is  used 
in  natural  philosophy,  is  not  known  in  pure 
mathematics.  There  certainly  are  instances  in 
which  a  general  proposition  is  proved  by  a  col- 
lection of  the  demonstrations  of  different  cases, 
which  may  remind  the  investigator  of  the  induc- 
tive process,  or  the  collection  of  the  general  from 
the  particular.  Such  instances  however  must 
not  be  taken  as  permanent,  for  it  usually  happens 
that  a  general  demonstration  is  discovered  as 
soon  as  attention  is  turned  to  the  subject. 

There  is  however  one  particular  method  of 
proceeding  which  is  extremely  common  in  math- 
ematical reasoning,  and  to  which  we  propose  to 
give  the  name  of  successive  induction.  It  has 
the  character  of  induction  as  defined  by  the  logi- 
cians, because  it  is  really  the  collection  of  a  gen- 
eral truth  from  a  demonstration  which  implies 
the  examination  of  every  particular  case  ;  but  it 
adds  to  the  necessary  character  of  induction  that 
each  case  depends  upon  one  or  more  of  those 
which  precede.  'Substituting  demonstration  for 
observation,  the  mathematical  process  is  truly 
inductive.  A  couple  of  instances  of  the  method 
will  enable  the  mathematical  reader  to  recognize 
a  mode  of  investigation  with  which  he  is  already 
familiar. 

Example  1. — The  sum  of  any  number  of  suc- 
cessive odd  numbers,  beginning  from  unity,  is  a 
square  number,  namely,  the  square  of  half  the 
even  number  which  follows  the  last  odd  number. 


QUOTATIONS   ON   INDUCTION.  303 

Let  this  proposition  be  true  in  any  one  single  in- 
stance ;  that  is,  n  being  some  whole  number,  let 
1,  3,  5  .  .  .  .  up  to  2n  +  l  put  together  give 
(n-f-1)2.  Then  the  next  odd  number  being 
2n  +  3,  the  sum  of  all  the  odd  numbers  up  to 
2n  +  3  will  be  (n+l)2-h  2  n  +  3,  or  n2+4n+4, 
or  (n+2)2.  But  n+2  is  the  half  of  the  even 
number  next  following  2n+3  :  consequently, 
if  the  proposition  be  true  of  any  one  set  of  odd 
numbers,  it  is  true  of  one  more.  But  it  is  true 
of  the  first  odd  number  1,  for  this  is  the  square 
of  half  the  even  number  next  following.  Conse- 
quently, being  true  of  1,  it  is  true  of  1+3  ;  be- 
ing true  of  1+3,  it  is  true  of  1+3+5  ;  being 
true  of  1+3+5,  it  is  true  of  1  +  3+5+7,  and 
so  on  ad  infinitum. 

Example  2. — The  formula  xn  —  &1,  n  being  a 
whole  number,  is  always  algebraically  divisible 
by  x — a. 

xn— an=xn— an~1x+an-1x— an 

=x(xn-1— an-1)+an~1  (x— a) 
In  this  last  expression  the  second   term  a  n-1 
(x— a)  is  obviously  divisible  by  x— a:  if  then 
any  one  of  the  succession 

x— a,  x2— a2,x3— a3,  x4— a4,  <fec. 
be  divisible  by  x— a,  so  is  the  next.     But  this  is 
obviously  true  of  the  first,  therefore  it  is  true  of 
the  second  ;  being  true  of  the  second,  it  is  true 
of  the  third  ;  and  so  on,  ad  infinitum. 

There  are  cases  in  which  the  successive  induc- 
tion only  brings  any  term  within  the  general  rule, 
when  two,  three,  or  more  of  the  terms  immedi- 
ately preceding  are  brought  within  it.  Thus 


304  QUOTATIONS   ON   INDUCTION. 

in  the  application  of  this  method  to  the  deduc- 
tion of  the  well  known  consequence  of 

x  H —  =  2  cos.  9, 
namely, 

xn  H =  2  cos.  n  6* 

xn 

it  can  only  be  shown  that  any  one  case  of  this 
theorem  is  true,  by  showing  that  the  preceding 
two  cases  are  true  ;  thus  its  truth,  when  n  =  5 
and  n  =  6,  makes  it  necessarily  follow  when 
n  =  7.  In  this  case  the  two  first  instances  must 
be  established  (when  n=l  by  hypothesis,  and 
when  n=2  by  independent  demonstration), 
which  two  establish  the  third,  the  second  and 
third  establish  the  fourth,  and  so  on. 

An  instance  of  mathematical  induction  occurs 
in  many  equations  of  differences,  in  every  recur- 
ring series,  etc. 

6.  From  Jevons'  Elementary  Lessons  in  Logic , 
pp.  208-28,  ed.  1878. 

To  express  the  difference  between  knowledge 
derived  deductively  and  that  obtained  induct- 
ively the  Latin  phrases  d  priori  and  a  pos- 
teriori are  often  used.  By  A  priori  reason- 
ing we  mean  argument  based  on  truths  pre- 
viously known ;  A  posteriori  reasoning,  on 
the  contrary,  proceeds  to  infer  from  the  conse- 
quences of  a  general  truth  what  that  gen- 
eral truth  is.  Many  philosophers  consider  that 
the  mind  is  naturally  in  possession  of  certain 


QUOTATIONS   ON  INDUCTION.  305 

laws  or  truths  which  it  must  recognise  in  every 
act  of  thought  ;  all  such,  if  they  exist,  would  be 
d  priori  truths.  It  cannot  be  doubted,  for  in- 
stance, that  we  must  always  recognise  in  thought 
the  three  Primary  Laws  of  Thought  considered 
in  Lesson  xiv.  We  have  there  an  d  priori 
knowledge  that  '  '  matter  cannot  both  have  weight 
and  be  without  weight, ' '  or  that  ' '  every  thing 
must  be  either  self-luminous  or  not  self-lumin- 
ous. "  But  there  is  no  law  of  thought  which 
can  oblige  us  to  think  that  matter  has  weight, 
and  luminous  ether  has  not  weight  ;  that  Jupiter 
and  Venus  are  not  self-luminous,  but  that  comets 
are  to  some  extent  self-luminous.  These  are 
facts  which  are  no  doubt  necessary  consequences 
of  the  laws  of  nature  and  the  general  constitution 
of  the  world  ;  but  as  we  are  not  naturally  ac- 
quainted with  all  the  secrets  of  creation,  we 
have  to  learn  them  by  observation,  or  by  the  d 
posteriori  method. 

It  is  not  however  usual  at  the  present  time 
to  restrict  the  name  d  priori  to  truths  obtained 
altogether  without  recourse  to  observation. 
Knowledge  may  originally  be  of  an  d  posteriori 
origin,  and  yet  having  been  long  in  possession, 
and  having  acquired  the  greatest  certainty,  it 
may  be  the  ground  of  deductions,  and  may  then 
be  said  to  give  d  priori  knowledge.  Thus  it  is 
now  believed  by  all  scientific  men  that  force 
cannot  be  created  or  destroyed  by  any  of  the 
processes  of  nature.  If  this  be  true  the  force 
which  disappears  when  a  bullet  strikes  a  target 
must  be  converted  into  something  else,  and  on 


306  QUOTATIONS   OK   INDUCTION. 

d  priori  grounds  we  may  assert  that  heat  will  be 
the  result.  It  is  true  that  we  might  easily  learn 
the  same  truth  d  posteriori,  by  picking  up  por- 
tions of  a  bullet  which  has  just  struck  a  target 
and  observing  that  they  are  warm.  But  there 
is  a  great  advantage  in  d  priori  knowledge  ;  we 
can  often  apply  it  in  cases  where  experiment  or 
observation  would  be  difficult.  If  I  lift  a  stone 
and  then  drop  it,  the  most  delicate  instruments 
could  hardly  show  that  the  stone  was  heated  by 
striking  the  earth  ;  yet  on  d  priori  grounds  I 
know  that  it  must  have  been  so,  and  can  easily 
calculate  the  amount  of  heat  produced.  Simi- 
larly we  know,  without  the  trouble  of  observa- 
tion, that  the  Falls  of  Niagara  and  all  other 
waterfalls  produce  heat.  This  is  fairly  an  in- 
stance of  d  priori  knowledge  because  no  one 
that  I  have  heard  of  has  tried  the  fact  or  proved 
it  d  posteriori;  nevertheless  the  knowledge  is 
originally  founded  on  the  experiments  of  Mr. 
Joule,  who  observed  in  certain  well-chosen  cases 
how  much  force  is  equivalent  to  a  certain  amount 
of  heat.  The  reader,  however,  should  take  care 
not  to  confuse  the  meaning  of  d  priori  thus  ex- 
plained with  that  given  to  the  words  by  the  phi- 
losophers who  hold  the  mind  to  be  in  the  pos- 
session of  knowledge  indepeudently  of  all  obser- 
vation. 

It  is  not  difficult  to  see  that  the  d  priori 
method  is  equivalent  to  the  synthetic  method 
considered  in  intension,  the  d  posteriori  method 
of  course  being  equivalent  to  the  analytic 
method.  But  the  same  difference  is  really  ex- 


QUOTATIONS   OX   INDUCTION.  307 

pressed  in  the  words  deductive  and  inductive  ; 
and  we  shall  frequently  need  to  consider  it  in 
the  following  lessons. 

PERFECT   INDUCTION   AND  THE   INDUCTIVE 
SYLLOGISM. 

WE  have  in  previous  lessons  considered  de- 
ductive reasoning,  which  consists  in  combining 
two  or  more  general  propositions  synthetically, 
and  thus  arriving  at  a  conclusion  which  is  a 
proposition  or  truth  of  less  generality  than  the 
premises,  that  is  to  say,  it  applies  to  fewer  indi- 
vidual instances  than  the  separate  premises  from 
which  it  was  inferred.  When  I  combine  the 
general  truth  that  "  metals  are  good  conductors 
of  heat, ' '  with  the  truth  that  i  i  aluminium  is  a 
metal, "  I  am  enabled  by  a  syllogism  in  the  mood 
Barbara  to  infer  that  l '  aluminium  is  a  good  con- 
ductor of  heat. ' '  As  this  is  a  proposition  con- 
cerning one  metal  only,  it  is  evidently  less  gen- 
eral than  the  premise,  which  referred  to  all 
metals  whatsoever.  In  induction,  on  the  con- 
trary, we  proceed  from  less  general,  or  even  from 
individual  facts,  to  more  general  propositions, 
truths,  or,  as  we  shall  often  call  them,  Laws  of 
Nature.  When  it  is  known  that  Mercury  moves 
in  an  elliptic  orbit  round  the  Sun,  as  also  Venus, 
the  Earth,  Mars,  Jupiter,  &c.,  we  are  able  to 
arrive  at  the  simple  and  general  truth  that  "  all 
the  planets  move  in  elliptic  orbits  round  the 
sun."  This  is  an  example  of  an  inductive  pro- 
cess of  reasoning. 

It  is  true   that  we  may  reason  without  ren- 


308  QUOTATIONS   ON   INDUCTION. 

dering  our  conclusion  either  more  or  less  general 
than  the  premises,  as  in  the  following  : — 
Snowdon  is  the  highest  mountain  in  England  or 

Wales. 

Snowdon  is  not  so  high  as  Ben  Nevis. 
Therefore  the  highest  mountain  in  England  or 

Wales  is  not  so  high  as  Ben  Nevis. 
Again  : 

Lithium  is  the  lightest  metal  known. 
Lithium  is  the  metal  indicated  by  one  bright  red 

line  in  the  spectrum.* 
Therefore  the  lightest  metal  known  is  the  metal 

indicated  by  a  spectrum  of  one  bright  red  line. 

In  these  examples  all  the  propositions  are 
singular  propositions,  and  merely  assert  the  iden- 
tity of  singular  terms,  so  that  there  is  no  altera- 
tion of  generality.  Each  conclusion  applies  to 
just  such  an  object  as  each  of  the  premises  applies 
to.  To  this  kind  of  reasoning  the  apt  name  of 
Traduction  has  been  given. 

Induction  is  a  much  more  difficult  and  more 
important  kind  of  reasoning  process  than  Tra- 
duction or  even  Deduction  ;  for  it  is  engaged  in 
detecting  the  general  laws  or  uniformities,  the 
relations  of  cause  and  effect,  or  in  short  all  the 
general  truths  that  may  be  asserted  concerning 
the  numberless  and  very  diverse  events  that  take 
place  in  the  natural  world  around  us.  The 
greater  part,  if  not,  as  some  philosophers  think, 
the  whole  of  our  knowledge,  is  ultimately  due  to 
inductive  reasoning.  The  mind,  it  is  plausibly 

*  Roscoe's  Lessons  in  Elementary  Chemistry,  p.  199. 


QUOTATIONS   ON   INDUCTION.  309 

said,  is  not  furnished  with  knowledge  in  the 
form  of  general  propositions  ready  made  and 
stamped  upon  it,  but  is  endowed  with  powers  of 
observation,  comparison,  and  reasoning,  which 
are  adequate,  when  well  educated  and  exercised, 
to  procure  knowledge  of  the  world  without  us 
and  the  worl  1  within  the  human  mind.  Even 
when  we  argue  synthetically  and  deductively 
from  simple  ideas  and  truths  which  seem  to  be 
ready  in  the  mind,  as  in  the  case  of  the  science 
of  geometry,  it  may  be  that  we  have  gathered 
those  simple  ideas  and  truths  from  previous  ob- 
servation or  induction  of  an  almost  unconscious, 
kind.  This  is  a  debated  point  upon  which  I 
will  not  here  speak  positively  ;  but  if  the  truth 
be  as  stated,  Induction  will  be  the  mode  by 
which  all  the  materials  of  knowledge  are  brought 
to  the  mind  and  analysed.  Deduction  wrill  then 
be  the  almost  equally  important  process  by 
which  the  knowledge  thus  acquired  is  utilised, 
and  by  which  new  Inductions  of  a  more  compli- 
cated character,  as  we  shall  see,  are  rendered 
possible. 

An  Induction,  that  is  an  act  of  Inductive 
reasoning,  is  called  Perfect  when  all  the  possible 
cases  or  instances  to  which  the  conclusion  can 
refer,  have  been  examined  and  enumerated  in  the 
premises.  If,  as  usually  happens,  it  is  impossi- 
ble to  examine  all  cases,  since  they  may  occur  at 
future  times  or  in  distant  parts  of  the  earth  or 
other  regions  of  the  universe,  the  Induction  is. 
called  Imperfect.  The  assertion  that  all  the 
months  of  the  year  are  of  less  length  than  thirty- 


310  QUOTATIONS   ON   INDUCTION. 

two  days  is  derived  from  Perfect  Induction,  and 
is  a  certain  conclusion  because  the  calendar  is  a 
human  institution,  so  that  we  know  beyond 
doubt  how  many  months  there  are,  and  can 
readily  ascertain  that  each  of  them  is  less  than 
thirty-two  days  in  length.  But  the  assertion 
that  all  the  planets  move  in  one  direction  round 
the  sun,  from  West  to  East,  is  derived  from  Im- 
perfect Induction  ;  for  it  is  possible  that  there 
exist  planets  more  distant  than  the  most  distant- 
known  planet  Neptune,  and  to  such  a  planet  of 
course  the  assertion  would  apply. 

Hence  it  is  obvious  that  there  is  a  great 
difference  between  Perfect  and  Imperfect  Induc- 
tion. The  latter  includes  some  process  by 
which  we  are  enabled  to  make  assertions  concern- 
ing things  that  we  have  never  seen  or  examined 
or  even  Known  to  exist.  But  it  must  be  care- 
fully remembered  also  that  no  Imperfect  Induc- 
tion can  give  a  certain  conclusion.  It  may  be 
highly  probable  or  nearly  certain  that  the  cases 
nnexamined  will  resemble  those  which  have  been 
examined,  but  it  can  never  be  certain.  It  is 
quite  possible,  for  instance,  that  a  new  planet 
might  go  round  the  sun  in  an  opposite  direction 
to  the  other  planets.  In  the  case  of  the  satel- 
lites belonging  to  the  planets  more  than  one  ex- 
ception of  this  kind  has  been  discovered,  and 
mistakes  have  constantly  occurred  in  science 
from  expecting  that  all  new  cases  would  exactly 
resemble  old  ones.  Imperfect  Induction  thus 
gives  only  a  certain  degree  of  probability  or  like- 
lihood that  all  instances  will  agree  with  those 


QUOTATIONS   ON  INDUCTION.  311 

examined.  Perfect  Induction,  on  the  other  hand, 
gives  a  necessary  and  certain  conclusion,  but  it 
asserts  nothing  beyond  what  was  asserted  in  the 
premises. 

Mr.  Mill,  indeed,  differs  from  almost  all  other 
logicians  in  holding  that  Perfect  Induction  is- 
improperly  called  Induction,  because  it  does  not 
lead  to  any  new  knowledge.  He  defines  In- 
duction as  inference  from  the  known  to  the  un- 
known, and  considers  the  unexamined  cases  which 
are  apparently  brought  into  our  knowledge  as  the 
only  gain  from  the  process  of  reasoning.  Hence 
Perfect  Induction  seems  to  him  to  be  of  no  scien- 
tific value  whatever,  because  the  conclusion  is  a 
mere  reassertion  in  a  briefer  form,  a  mere  sum- 
ming up  of  the  premises.  I  may  point  out,  how- 
ever, that  if  Perfect  Induction  were  no  more 
than  a  process  of  abbreviation  it  is  yet  of  great 
importance,  and  requires  to  be  continually  used 
hi  science  and  common  life.  Without  it  we 
could  never  make  a  comprehensive  statement, 
but  should  be  obliged  to  enumerate  every  partic- 
ular. After  examining  the  books  in  a  library 
and  finding  them  to  be  all  English  books  we 
should  be  unable  to  sum  up  our  results  in  the 
one  proposition,  "  all  the  books  in  this  library 
are  English  books  ;"  but  should  be  required  to  go 
over  the  list  of  books  every  time  we  desired  to 
make  any  one  acquainted  with  the  contents  of 
the  library.  The  fact  is,  that  the  power  of  ex- 
pressing a  great  number  of  particular  facts  in  a 
very  brief  space  is  essential  to  the  progress  of 
science.  Just  as  the  whole  science  of  arithmetic 


312  QUOTATIONS   ON   INDUCTION. 

consists  in  nothing  but  a  series  of  processes  for 
abbreviating  addition  and  subtraction,  and  enab- 
ling us  to  deal  with  a  great  number  of  units  in  a 
very  short  time,  so  Perfect  Induction  is  abso- 
lutely necessary  to  enable  us  to  deal  with  a  great 
number  of  particular  facts  in  a  very  brief  space. 

It  is  usual  to  represent  Perfect  Induction  in 
the  form  of  an  Inductive  Syllogism,  as  in  the 
following  instance  : — 
Mercury,  Venus,  the  Earth,  &c.,  all  move  round 

the  sun  from  West  to  East. 
Mercury,   Venus,    the    Earth,    &c.,  are    all    the 

known  Planets. 
Therefore  all  the  known  planets  move  round  the 

sun  from  AVest  to  East. 

This  argument  is  a  true  Perfect  Induction 
because  the  conclusion  only  makes  an  assertion 
of  all  known  planets,  which  excludes  all  refer- 
ence to  possible  future  discoveries  ;  and  we  may 
suppose  that  all  the  known  planets  have  been 
enumerated  in  the  premises.  .  .  . 

As  another  example  of  a  Perfect  Induction 
we  may  take — 

January,  February, December,  each  con- 
tain less  than  32  days. 
January December  are  all  the  months  of 

the  year. 
Therefore  all  the  months  of  the  year  contain  less 

than  32  days. 

Although  Sir  W.  Hamilton  has  entirely 
rejected  the  notion,  it  seems  worthy  of  inquiry 
whether  the  Inductive  Syllogism  be  not  really  of 
the  Disjunctive  form  of  Syllogism.  Thus  I 


QUOTATIONS   ON   INDUCTION.  313 

should  be  inclined  to  represent  the  last  example 
in  the  form  : 

A  month  of  the  year  is  either  January,   or 

February,  or  March or  December  ;  but 

January  has  less  than  32  days  ;  and  February  has 
less  than  32  days  ;  and  so  on  until  we  come  to 
December,  which  has  less  than  32  days. 

It  follows  clearly  that  a  month  must  in  any 
case  have  less  than  32  days  ;  for  there  are  only 
12  possible  cases,  and  in  each  case  this  is  affirm- 
ed. The  fact  is  that  the  major  premise  of  the 
syllogism  on  the  last  page  is  a  compound  sen- 
tence with  twelve  subjects,  and  is  therefore  equi- 
valent to  twelve  distinct  logical  propositions. 
The  minor  premise  is  either  a  disjunctive  propo- 
sition, as  I  have  represented  it,  or  something 
quite  different  from  anything  we  have  elsewhere 
had. 

From  Perfect  Induction  we  shall  have  to 
pass  to  Imperfect  Induction ;  but  the  opinions 
of  Logicians  are  not  in  agreement  as  to  the 
grounds  upon  which  we  are  warranted  in  taking 
a  part  of  the  instances  only,  and  concluding  that 
what  is  true  of  those  is  true  of  all.  Thus  if  we 
adopt  the  example  found  in  many  books  and 
say — 

This,  that,  and  the  other  magnet  attract  iron  ; 
This,  that,  and  the  other  magnet  are  all  magnets  ; 
Therefore  all  magnets  attract  iron, 
we  evidently  employ  a  false  minor  premise,  be- 
cause this,  that,  and  the  other  magnet  which  we 
have  examined,   cannot  possibly  be  all  existing 
magnets.      In  whatever  form  we  put  it  there 


314  QUOTATIONS   ON   INDUCTION. 

must  be  an  assumption  that  the  magnets  which 
we  have  examined  are  a  fair  specimen  of  all 
magnets,  so  that  what  we  find  in  some  we  may 
expect  in  all.  Archbishop  Whately  con- 
siders that  this  assumption  should  be  expressed 
in  one  of  the  premises,  and  he  represents  Induc- 
tion as  a  Syllogism  as  follows  : — 
That  which  belongs  to  this,  that,  and  the  other 

magnet,  belongs  to  all  ; 
Attracting  iron  belongs  to  this,   that,   and  the 

other  ; 

Therefore  it  belongs  to  all. 

But  though  this  is  doubtless  a  correct  expression 
of  the  assumption  made  in  an  Imperfect  Induc- 
tion, it  does  not  in  the  least  explain  the  grounds 
on  which  we  are  allowed  to  make  the  assump- 
tion, and  under  what  circumstances  such  an  as- 
sumption would  be  likely  to  prove  true.  Some 
writers  have  asserted  that  there  is  a  Principle 
called  the  Uniformity  of  Nature,  which  enables 
us  to  affirm  that  what  has  often  been  found  to 
be  true  of  anything  will  continue  to  be  found 
true  of  the  same  sort  of  thing.  It  must  be  ob- 
served, however,  that  if  there  be  such  a  principle 
it  is  liable  to  exceptions  ;  for  many  facts  which 
have  held  true  up  to  a  certain  point  have  after- 
wards  been  found  not  to  be  always  true.  Thus 
there  was  a  wide  and  unbroken  induction  tend- 
ing to  show  that  all  the  Satellites  in  the  plane- 
tary system  went  in  one  uniform  direction  round 
their  planets.  Nevertheless  the  Satellites  of 
Uranus  when  discovered  were  found  to  move  in 
a  retrograde  direction,  or  in  an  opposite  direction 


QUOTATIONS   ON  INDUCTION.  315 

to  all  Satellites  previously  known,  and  the  same 
peculiarity  attaches  to  the  Satellite  of  Neptune 
more  lately  discovered. 

We  may  defer  to  the  next  lesson  the  ques- 
tion of  the  varying  degree  of  certainty  which  be- 
longs to  induction  in  the  several  branches  of 
knowledge. 

The  advanced  student  may  consult  the  fol- 
lowing with  advantage  : — Hansel's  Aldrich,  Ap- 
pendix, Notes  G  and  H.  Hamilton's  Lectures 
on  Logic,  Lecture  xvn.,  and  Appendix  vn.,  On 
Induction  and  Example,  Vol.  n.,  p.  358.  J.  S. 
Mill's  System  of  Logic,  Book  in.  Chap.  2,  Of 
Inductions  improperly  so-called. 

GEOMETKICAL    AND    MATHEMATICAL    INDUC- 
TION, ANALOGY  AND  EXAMPLE. 

IT  is  now  indispensable  that  we  should  con- 
sider with  great  care  upon  what  grounds  Imper- 
fect Induction  is  founded.  No  difficulty  is  en- 
countered in  Perfect  Induction  because  all  possi- 
ble cases  which  can  come  under  the  general  con- 
clusion are  enumerated  in  the  premises,  so  that 
in  fact  there  is  no  information  in  the  conclusion 
which  was  not  given  in  the  premises.  In  this 
respect  the  Inductive  Syllogism  perfectly  agrees 
with  the  general  principles  of  deductive  reason- 
ing, which  require  that  the  information  contain- 
ed in  the  conclusion  should  be  shown  only  from 
the  data,  and  that  we  should  merely  unfold,  or 
transform  into  an  explicit  statement  what  is  con- 
tained in  the  premises  implicitly. 

In  Imperfect  Induction  the  process  seems  to 


316  QUOTATIONS   ON   INDUCTION. 

be  of  a  wholly  di  fferent  character,  since  the  in- 
stances concerning  which  we  acquire  knowledge 
may  be  infinitely  more  numerous  than  those  from 
which  we  acquire  the  knowledge.  Let  us  con- 
sider in  the  first  place  the  process  of  Geometrical 
Reasoning  which  has  a  close  resemblance  to  in- 
ductive reasoning.  When  in  the  fifth  proposi- 
tion of  the  first  book  of  Euclid  we  prove  that 
the  angles  at  the  base  of  an  isosceles  triangle  are 
equal  to  each  other,  it  is  done  by  taking  one  par- 
ticular triangle  as  an  example.  A  figure  is  given 
which  the  reader  is  requested  to  regard  as  having 
two  equal  sides,  and  it  is  conclusively  proved 
that  if  the  sides  be  really  equal  then  the  angles 
opposite  to  those  sides  must  be  equal  also.  But 
Euclid  says  nothing  about  other  isosceles  trian- 
gles ;  he  treats  one  single  triangle  as  a  sufficient 
specimen  of  all  isosceles  triangles,  and  we  are 
asked  to  believe  that  what  is  true  of  that  is  true 
of  any  other,  whether  its  sides  be  so  small  as  to 
be  only  visible  in  a  microscope,  or  so  large  as  to 
reach  to  the  furthest  fixed  star.  There  may  evi- 
dently be  an  infinite  number  of  isosceles  trian- 
gles as  regards  the  length  of  the  equal  sides,  and 
each  of  these  may  be  infinitely  varied  by  increas- 
ing or  diminishing  the  contained  angle,  so  that 
the  number  of  possi-ble  isosceles  triangles  is  infi- 
nitely infinite  ;  and  yet  we  are  asked  to  believe 
of  this  incomprehensible  number  of  objects  what 
we  have  proved  only  of  one  single  specimen. 
This  might  seem  to  be  the  most  extremely  Im- 
perfect Induction  possible,  and  yet  every  one  al- 
lows that  it  gives  us  really  certain  knowledge. 


QUOTATIONS   ON   INDUCTION.  317 

We  do  know  with  as  much  certainty  as  knowl- 
edge can  possess,  that  if  lines  be  conceived  as 
drawn  from  the  earth  to  two  stars  equally  dis- 
tant, they  will  make  equal  angles  with  the  line 
joining  those  stars  ;  and  yet  we  can  never  have 
tried  the  experiment. 

The  generality  of  this  geometrical  reasoning 
evidently  depends  upon  the  certainty  with  which 
we  know  that  all  isosceles  triangles  exactly  resem- 
ble each  other.  The  proposition  proved  does 
not  in  fact  apply  to  a  triangle  unless  it  agrees 
with  our  specimen  in  all  the  qualities  essential  to 
the  proof.  The  absolute  length  of  any  of  the 
sides  or  the  absolute  magnitude  of  the  angle  con- 
tained between  any  of  them  were  not  points 
upon  which  the  proof  depended — they  were 
purely  accidental  circumstances  ;  hence  we  are 
at  perfect  liberty  to  apply  to  all  new  cases  of  an 
isosceles  triangle  what  we  learn  of  one  case. 
Upon  a  similar  ground  rests  all  the  vast  body  of 
certain  knowledge  contained  in  the  mathematical 
sciences — not  only  all  the  geometrical  truths,  but 
all  general  algebraical  truth.  It  was  shown,  for 
instance,  in  p.  58,  that  if  a  and  b  be  two  quan- 
tities, and  we  multiply  together  their  sum  and 
difference,  we  get  the  difference  of  the  squares 
of  a  and  b.  However  often  we  try  this  it  will 
be  found  true  ;  thus  if  a=10  and  6=7,  the  prod- 
uct of  the  sum  and  difference  is  17x3  =  51  ; 
the  squares  of  the  quantities  are  10x10  or  100 
and  7x7  or  49,  the  difference  of  which  is  also 
51.  But  however  often  we  tried  the  rule  no 
certainty  would  be  added  to  it  ;  because  when 


318  QUOTATIONS   ON   INDUCTION. 

proved  algebraically  there  was  no  condition 
which  restricted  the  result  to  any  particular  num- 
bers, and  a  and  b  might  consequently  be  auy 
numbers  whatever.  This  generality  of  algebraical 
reasoning  by  which  a  property  is  proved  of  infi- 
nite varieties  of  numbers  at  once,  is  one  of  the 
chief  advantages  of  algebra  over  arithmetic. 
There  is  also  in  algebra  a  process  called  Mathe- 
matical Induction  or  Demonstrative  Induction, 
which  shows  the  powers  of  reasoning  in  a  very 
conspicuous  way.  A  good  example  is  found  in 
the  following  problem  :  —  If  we  take  the  first  two 
consecutive  odd  numbers,  1  and  3,  and  add  them 
together  the  sum  is  4,  or  exactly  twice  two  ;  if  we 
take  three  such  numbers  l-)-3-j-5,  the  sum  is  9 
or  exactly  three  times  three  ;  if  we  take  four, 
namely  l-|~3+5-|-7  the  sum  is  16,  or  exactly 
four  times  four  ;  or  generally,  if  we  take  any 
given  number  of  the  series,  l-[-3+5-|-7+... 
the  sum  is  equal  to  the  number  of  the  terms  mul- 
tiplied by  itself.  Anyone  who  knows  a  very 
little  algebra  can  prove  that  this  remarkable  law 
is  universally  true,  as  follows  —  Let  n  be  the 
number  of  terms,  and  assume  for  a  moment  that 
this  law  is  true  up  to  n  terms,  thus  — 

1+3  +  5  +  7+  ......  +  (2  n—  1)  =  n\ 

Now  add  2n  +  1  to  each  side  of  the  equation. 
It  follows  that  — 


1+3  +  5  +  7+ 

=  n* 

But    the    last    quantity   ri*  -\-2n-\-\    is   just 


QUOTATIONS   ON   INDUCTION.  319 

equal  to  (n-\-iy  ;  so  that  if  the  law  is  true  for  n 
terms  it  is  true  also  for  n-\-l  terms.  We  are 
enabled  to  argue  from  each  single  case  of  the 
law  to  the  next  case  ;  but  we  have  already  shown 
that  it  is  true  of  the  first  few  cases,  therefore  it 
must  be  true  of  all.  By  no  conceivable  labor 
could  a  person  ascertain  by  trial  what  is  the  sum 
of  the  first  billion  odd  numbers,  and  yet  symbol- 
ically or  by  general  reasoning  we  know  with  cer- 
tainty that  they  would  amount  to  a  billion  bil- 
lion, and  neither  more  nor  less  even  by  a  unit. 
This  process  of  Mathematical  Induction  is  not 
exactly  the  same  as  Geometrical  Induction,  be- 
cause each  case  depends  upon  the  last,  but  the 
proof  rests  upon  an  equally  narrow  basis  of  ex- 
perience, and  creates  knowledge  of  equal  cer- 
tainty and  generality. 

Such  mathematical  truths  depend  upon  ob- 
servation of  a  few  cases,  but  they  acquire  cer- 
tainty from  the  perception  we  have  of  the  exact 
similarity  of  one  case  to  another,  so  that  we  un- 
doubtingly  believe  what  is  true  of  one  case  to  be 
true  of  another.  It  is  very  instructive  to  con- 
trast with  these  cases  certain  other  ones  where 
there  is  a  like  ground  of  observation,  but  not 
the  same  tie  of  similarity.  It  was  at  one  time 
believed  that  if  any  integral  number  were  multi- 
pled  by  itself,  added  to  itself  and  then  added 
to  41,  the  result  would  be  a  prime  number,  that 
is  a  number  which  could  not  be  divided  by  any 
other  integral  number  except  unity  ;  in  symbols, 

x2  +  x  +  41  =  prime  number. 


320  QUOTATIONS   ON   INDUCTION. 

This  was  believed  solely  on  the  ground  of 
trial,  and  experience,  and  it  certainly  holds  for  a 
great  many  values  of  x.  Thus  when  x  is  suc- 
cessively made  equal  to  the  numbers  in  the  first 
line  below,  the  expression  x*  -\-x-\- 41  gives  the 
values  in  the  second  line,  and  they  are  all  prime 
numbers  : 

0123456789       10 
41     43    47     53     61     71     83     97   113  131   151 

No  reason  however  could  be  given  why  it 
should  always  be  true,  and  accordingly  it  was 
found  that  the  rule  does  not  always  hold  true, 
but  fails  when  #=40.  Then  we  have  40x40 
_j_40-|-41=:1681,  but  this  is  clearly  equal  to 
41  X40-J-41  or  41  X41,  and  is  not  a  prime  num- 
ber. 

In  that  branch  of  mathematics  which  treats 
of  the  peculiar  properties  and  kinds  of  numbers, 
other  propositions  depending  solely  upon  obser- 
vation have  been  asserted  to  be  always  true. 

z 

Thus  Fermat  believed  that  22-|-l  always  repre- 
sents a  prime  number,  but  could  not  give  any 
reason  for  the  assertion.  It  holds  true  in  fact 
until  the  product  reaches  the  large  number 
4294967297,  which  was  found  to  be  divisible  by 
641,  so  that  the  generality  of  the  statement  was 
disproved. 

We  find  then  that  in  some  cases  a  single  in- 
stance proves  a  general  and  certain  rule,  while 
in  others  a  very  great  number  of  instances  are 
insufficient  to  give  any  certainty  at  all  ;  all  de- 


QUOTATIONS   OK   INDUCTION'.  321 

pends  upon  the  perception  we  have  of  similarity 
or  identity  between  one  case  and  another.  We 
can  perceive  no  similarity  between  all  prime 
numbers  which  assures  us  that  because  one  is 
represented  by  a  certain  formula,  also  another 
is  ;  but  we  do  find  such  similarity  between  the 
sums  of  odd  numbers,  or  between  isosceles  tri- 
angles. 

Exactly  similar  considerations  apply  to  induc- 
tions in  physical  science.  When  a  chemist  an- 
alyses a  few  grains  of  water  and  finds  that  they 
contain  exactly  8  parts  of  oxygen  and  1  of  hy- 
drogen for  9  parts  of  water,  he  feels  warranted  in 
asserting  that  the  same  is  true  of  all  pure  water 
whatever  be  its  origin,  and  whatever  be  the  part 
of  the  world  from  which  it  comes.  But  if  he 
analyse  a  piece  of  granite,  or  a  sample  of  sea- 
water  from  one  part  of  the  world,  he  does  not 
feel  any  confidence  that  it  will  resemble  exactly 
a  piece  of  granite,  or  a  sample  of  sea- water  from 
another  part  of  the  earth  ;  hence  he  does  not 
venture  to  assert  of  all  granite  or  sea- water,  what 
he  finds  true  of  a  single  sample.  Extended  ex- 
perience shows  that  granite  is  very  variable  in 
composition,  but  that  sea-water  is  rendered 
pretty  uniform  by  constant  mixture  of  currents. 
Nothing  but  experience  in  these  cases  could  in- 
form us  how  far  we  may  assert  safely  of  one 
sample  what  we  have  ascertained  of  another. 
But  we  have  reason  to  believe  that  chemical 
compounds  are  naturally  fixed  and  invariable  in 
composition,  according  to  Dalton's  laws  of  com- 
bining proportions.  No  d  priori  reasoning  from 


322  QUOTATIONS   ON   INDUCTION. 

the  principles  of  thought  could  have  told  us  this, 
and  we  only  learn  it  by  extended  experiment. 
But  having  once  shown  it  to  be  true  with  certain 
substances  we  do  not  need  to  repeat  the  trial 
with  all  other  substances,  because  we  have  every 
reason  to  believe  that  it  is  a  natural  law  in  which 
all  chemical  substances  resemble  each  other.  It 
is  only  necessary  then  for  a  single  accurate  anal- 
ysis of  a  given  fixed  compound  to  be  made  in 
order  to  inform  us  of  the  composition  of  all 
other  portions  of  the  same  substance. 

It  must  be  carefully  observed  however  that 
all  inductions  in  physical  science  are  only 
probable,  or  that  if  certain,  it  is  only  hypotheti- 
cal certainty  they  possess.  Can  I  be  absolutely 
certain  that  all  water  contains  one  part  of  hydro- 
gen in  nine  ?  I  am  certain  only  on  two  condi- 
tions : — 

1 .  That  this  was  certainly  the  composition  of 
the  sample  tried. 

2.  That  any  other  substance  I  call  water  ex- 
actly resembles  that  sample. 

But  even  if  the  first  condition  be  undoubtedly 
true,  1  cannot  be  certain  of  the  second.  For  how 
do  I  know  what  is  water  except  by  the  fact  of 
its  being  a  transparent  liquid,  freezing  into  a 
:  solid  and  evaporating  into  steam,  possessing  a 
high  specific  heat,  and  a  number  of  other  dis- 
tinct properties  ?  But  can  I  be  absolutely  cer- 
tain that  every  liquid  possessing  all  these  proper- 
ties is  water  ?  Practically  I  can  be  certain,  but 
theoretically  I  cannot. 


QUOTATION'S   Otf   INDUCTION.  323 

V.  From  Mill's  System  of  Logic,  pp.  125,  126  : 
210-228,  8vo  edition. 

Reasoning,  in  the  extended  sense  in  which  I 
use  the  term,  and  in  which  it  is  synonymous 
with  Inference,  is  popularly  said  to  be  of  two 
kinds  :  reasoning  from  particulars  to  generals, 
and  reasoning  from  generals  to  particulars  ; 
the  former  being  called  Induction,  the  latter 
Ratiocination  or  Syllogism.  It  will  presently 
be  shown  that  there  is  a  third  species  of  rea- 
soning, which  falls  under  neither  of  these  de- 
scriptions, and  which,  nevertheless*  is  not  only 
valid,  but  is  the  foundation  of  both  the 
others.  ...  Of  Induction,  therefore,  we 
shall  say  no  more  at  present,  than  that  it  at  least 
is,  without  doubt,  a  process  of  real  inference. 
The  conclusion  in  an  induction  embraces  more 
than  is  contained  in  the  premises.  The  principle 
or  law  collected  from  particular  instances,  the 
general  proposition  in  which  we  embody  the  re- 
sult of  our  experience,  covers  a  much  larger  ex- 
tent of  ground  than  the  individual  experiments 
which  form  its  basis.  A  principle  ascertained  by 
experience,  is  more  than  a  mere  summing  up  of 
what  has  been  specifically  observed  in  the  indi- 
vidual cases  which  have  been  examined  ;  it  is  a 
generalization  grounded  on  those  cases,  and  ex- 
pressive of  our  belief,  that  what  we  there  found 
true  is  true  in  an  indefinite  number  of  cases 
which  we  have  not  examined,  and  are  never 
likely  to  examine.  The  nature  and  grounds  of 
this  inference,  and  the  conditions  necessary  to 
make  it  legitimate,  will  be  the  subject  of  discus- 


324  QUOTATIONS   OK   INDUCTION. 

sion  in  the  Third  Book  :  but  that  such  inference 
really  takes  place  is  not  susceptible  of  question. 
In  every  induction  we  proceed  from  truths  which 
we  knew,  to  truths  which  we  did  not  know  ; 
from  facts  certified  by  observation,  to  facts 
which  we  have  not  observed,  and  even  to  facts 
not  capable  of  being  now  observed ;  future 
facts,  for  example  ;  but  which  we  do  not  hesi- 
tate to  believe  on  the  sole  evidence  of  the  induc- 
tion itself.  Induction,  then,  is  a  real  process  of 
Reasoning  or  Inference. 

OF    INDUCTIONS    IMPROPERLY    SO    CALLED. 

§  1.  Induction,  then,  is  that  operation  of  the 
mind,  by  which  we  infer  that  what  we  know  to  be 
true  in  a  particular  case  or  cases,  will  be  true  in  all 
cases  which  resemble  the  former  in  certain  assign- 
able respects.  In  other  words,  Induction  is  the 
process  by  which  we  conclude  that  what  is  true 
of  certain  individuals  of  a  class  is  true  of  the 
whole  class,  or  that  what  is  true  at  certain  times 
will  be  true  in  similar  circumstances  at  all  times. 

This  definition  excludes  from  the  meaning  of 
the  term  Induction,  various  logical  operations,  to 
which  it  is  not  unusual  to  apply  that  name. 

Induction,  as  above  defined,  is  a  process  of 
inference-;  it  proceeds  from  the  known  to  the 
unknown  ;  and  any  operation  involving  no  infer- 
ence, any  process  in  which  what  seems  the  con- 
clusion is  no  wider  than  the  premises  from  which 
it  is  drawn,  does  not  fall  within  the  meaning  of 
the  term.  Yet  in  the  common  books  of  Logic 
we  find  this  laid  down  as  the  most  perfect,  in- 


QUOTATIONS   OK   INDUCTION.  325 

deed  the  only  quite  perfect,  form  of  induction. 
In  those  books,  every  process  .which  sets  out 
from  a  less  general  and  terminates  in  a  more 
general  expression — which  admits  of  being  stated 
in  the  form,  "  This  and  that  A  are  B,  therefore 
every  A  is  B  " — is  called  an  induction,  whether 
any  thing  be  really  concluded  or  not  :  and  the 
induction  is  asserted  not  to  be  perfect,  unless 
every  single  individual  of  the  class  A  is  included 
in  the  antecedent,  or  premise  :  that  is,  unless 
what  we  affirm  of  the  class  has  already  been  as- 
certained to  be  true  of  every  individual  in  it,  so- 
that  the  nominal  conclusion  is  not  really  a  con- 
clusion, but  a  mere  re-assertion  of  the  premises. 
If  we  were  to  say,  All  the  planets  shine  by  the 
sun's  light,  from  observation  of  each  separate 
planet,  or  All  the  Apostles  were  Jews,  because 
this  is  true  of  Peter,  Paul,  John,  and  every  other 
apostle — these,  and  such  as  these,  would,  in  the 
phraseology  in  question,  be  called  perfect,  and 
the  only  perfect,  Inductions.  This,  however,  is 
a  totally  different  kind  of  induction  from  ours  ; 
it  is  not  an  inference  from  facts  known  to  facts 
unknown,  but  a  mere  short-hand  registration  of 
facts  known.  The  two  simulated  arguments 
which  we  have  quoted,  are  not  generalizations  ; 
the  propositions  purporting  to  be  conclusions 
from  them,  are  not  really  general  propositions. 
A  general  proposition  is  one  in  which  the  predi- 
cate is  affirmed  or  denied  of  an  unlimited  num- 
ber of  individuals  ;  namely,  all,  whether  few  or 
many,  existing  or  capable  of  existing,  which  pos- 
sess the  properties  connoted  by  the  subject  of 


326  QUOTATIONS   ON   INDUCTION. 

the  proposition.  i  l  All  men  are  mortal ' '  does 
not  mean  all  now  living,  but  all  men  past,  pres- 
ent, and  to  come.  When  the  signification  of 
the  term  is  limited  so  as  to  render  it  a  name  not 
for  any  and  every  individual  falling  under  a  cer- 
tain general  description,  but  only  for  each  of  a 
number  of  individuals,  designated  as  such,  and 
as  it  were,  counted  off  individually,  the  proposi- 
tion, though  it  may  be  general  in  its  language, 
is  no  general  proposition,  but  merely  that  num- 
ber of  singular  propositions,  written  in  an  abridg- 
ed character.  The  operation  may  be  very  use- 
ful, as  most  forms  of  abridged  notation  are  ; 
but  it  is  no  part  of  the  investigation  of  truth, 
though  often  bearing  an  important  part  in  the 
preparation  of  the  materials  for  that  investiga- 
tion. 

As  we  may  sum  up  a  definite  number  of  singular 
propositions  in  one  proposition,  which  will  be 
apparently,  but  not  really,  general,  so  we  may 
sum  up  a  definite  number  of  general  proposi- 
tions in  one  proposition,  which  will  be  apparent- 
ly, but  not  really,  more  general.  If  by  a  sepa- 
rate induction  applied  to  every  distinct  species  of 
animals,  it  has  been  established  that  each  pos- 
sesses a  nervous  system,  and  we  affirm  thereupon 
that  all  animals  have  a  nervous  system  ;  this  looks 
like  a  generalization,  though  as  the  conclusion 
merely  affirms  of  all  what  has  already  been  af- 
firmed of  each,  it  seems  to  tell  us  nothing  but  what 
we  knew  before.  A  distinction,  however,  must 
be  made.  If  in  concluding  that  all  animals  have 
a  nervous  system,  we  mean  the  same  thing  and 


QUOTATIONS   ON   INDUCTION.  32? 

no  more  as  if  we  had  said  "  all  known  animals, " 
the  proposition  is  not  general,  and  the  process 
by  which  it  is  arrived  at  is  not  induction.  But 
if  our  meaning  is  that  the  observations  made  of 
the  various  species  of  animals  have  discovered  to 
us  a  law  of  animal  nature,  and  that  we  are  in  a 
condition  to  say  that  a  nervous  system  will  be 
found  even  in  animals  yet  undiscovered,  this  in- 
deed is  an  induction  ;  but  in  this  case  the  general 
proposition  contains  more  than  the  sum  of  the 
special  propositions  from  which  it  is  inferred. 
The  distinction  is  still  more  forcibly  brought  out 
when  we  consider,  that  if  this  real  generalization 
be  legitimate  at  all,  its  legitimacy  probably  does 
not  require  that  we  should  have  examined  with- 
out exception  every  known  species.  It  is  the 
number  and  nature  of  the  instances,  and  not  their 
being  the  whole  of  those  which  happen  to  be 
known,  that  makes  them  sufficient  evidence  ta 
prove  a  general  law  :  while  the  more  limited  as- 
sertion, which  stops  at  all  known  animals,  cannot 
be  made  unless  we  have  rigorously  verified  it  in 
every  species.  In  like  manner  (to  return  to  a 
former  example)  we  might  have  inferred,  not  that 
all  the  planets,  but  that  all  planets,  shine  by  re- 
flected light :  the  former  is  no  induction  ;  the 
latter  is  an  induction,  and  a  bad  one,  being  dis- 
proved by  the  case  of  double  stars — self-lum- 
inous bodies  which  are  properly  planets,  since 
they  revolve  round  a  centre. 

§  2.  There  are  several  processes  used  in  math- 
ematics which  require  to  be  distinguished  from 
Induction,  being  not  unfrequently  called  by  that 


328  QUOTATIONS   ON   INDUCTION. 

name,  and  being  so  far  similar  to  Induction 
properly  so  called,  that  the  propositions  they 
lead  to  are  really  general  propositions.  For  ex- 
ample, when  we  have  proved  with  respect  to 
the  circle,  that  a  straight  line  can  not  meet  it  in 
more  than  two  points,  and  when  the  same  thing 
has  been  successively  proved  of  the  ellipse,  the 
parabola,  and  the  hyperbola,  it  may  be  laid 
down  as  a  universal  property  of  the  sections  of 
the  cone.  The  distinction  drawn  in  the  two 
previous  examples  can  have  no  place  here,  there 
being  no  difference  between  all  known  sections 
of  the  cone  and  all  sections,  since  a  cone  demon- 
strably  can  not  be  intersected  by  a  plane  except 
in  one  of  these  four  lines.  It  would  be  diffi- 
cult, therefore,  to  refuse  to  the  proposition  ar- 
rived at,  the  name  of  a  generalization,  since 
there  is  no  room  for  any  generalization  beyond 
it.  But  there  is  no  induction,  because  there  is 
no  inference  :  the  conclusion  is  a  mere  summing 
up  of  what  was  asserted  in  the  various  proposi- 
tions from  which  it  is  drawn.  A  case  some- 
what, though  not  altogether,  similar,  is  the  proof 
of  a  geometrical  theorem  by  means  of  a  diagram. 
Whether  the  diagram  be  on  paper  or  only  in  the 
imagination,  the  demonstration  (as  formerly  ob- 
served) does  not  prove  directly  the  general  theo- 
rem ;  it  proves  only  that  the  conclusion,  which 
the  theorem  asserts  generally,  is  true  of  the  par- 
ticular triangle  or  circle  exhibited  in  the  diagram  ; 
but  since  we  perceive  that  in  the  same  way  in 
which  we  have  proved  it  of  that  circle,  it  might 
also  be  proved  of  any  other  circle,  we  gather  up 


QUOTATIONS  O:NT  INDUCTION.         329 

into  one  general  expression  all  the  singular  prop- 
ositions susceptible  of  being  thus  proved,  arid 
embody  them  in  a  universal  proposition.  Hav- 
ing shown  that  the  three  angles  of  the  triangle 
ABC  are  together  equal  to  two  right  angles,  we 
conclude  that  this  is  true  of  every  other  triangle, 
not  because  it  is  true  of  ABC,  but  for  the  same 
reason  which  proved  it  to  be  true  of  ABC.  If 
this  were  to  be  called  Induction,  an  appropriate 
name  for  it  would  be,  induction  by  parity  of  rea- 
soning. But  the  term  can  not  properly  belong 
to  it  ;  the  characteristic  quality  of  Induction  is 
wanting,  since  the  truth  obtained,  though  really 
general,  is  not  believed  on  the  evidence  of  par- 
ticular instances.  We  do  not  conclude  that  all 
triangles  have  the  property  because  some  trian- 
gles have,  but  from  the  ulterior  demonstrative 
evidence  which  was  the  ground  of  our  conviction 
in  the  particular  instances. 

There  are  nevertheless,  in  mathematics,  some 
examples  of  so-called  Induction,  in  which  the 
conclusion  does  bear  the  appearance  of  a  gener- 
alization grounded  on  some  of  the  particular 
cases  included  in  it.  A  mathematician,  when  he 
has  calculated  a  sufficient  number  of  the  terms  of 
an  algebraical  or  arithmetical  series  to  have  ascer- 
tained what  is  called  the  law  of  the  series,  does 
not  hesitate  to  fill  up  any  number  of  the  suc- 
ceeding terms  without  repeating  the  calculations. 
But  I  apprehend  he  only  does  so  when  it  is  appa- 
rent from  a  priori  considerations  (which  might 
be  exhibited  in  the  form  of  demonstration)  that 
the  mode  of  formation  of  the  subsequent  terms, 


330  QUOTATIONS   OK   INDUCTION. 

each  from  that  which  preceded  it,  must  be  simi- 
lar to  the  formation  of  the  terms  which  have 
been  already  calculated.  And  when  the  attempt 
has  been  hazarded  without  the  sanction  of  such 
general  considerations,  there  are  instances  on  rec- 
ord in  which  it  has  led  to  false  results. 

It  is  said  that  Newton  discovered  the  binomial 
theorem  by  induction  ;  by  raising  a  binomial 
successively  to  a  certain  number  of  powers,  and 
comparing  those  powers  with  one  another  until 
he  detected  the  relation  in  which  the  algebraic 
formula  of  each  power  stands  to  the  exponent  of 
that  power,  and  to  the  two  terms  of  the  bino- 
mial. The  fact  is  not  improbable  :  but  a  math- 
ematician like  Newton,  who  seemed  to  arrive  per 
saltum  at  principles  and  conclusions  that  ordinary 
mathematicians  only  reached  by  a  succession  of 
steps,  certainly  could  not  have  performed  the 
comparison  in  question  without  being  led  by  it 
to  the  a  priori  ground  of  the  law  ;  since  any  one 
who  understands  sufficiently  the  nature  of  multi- 
plication to  venture  upon  multiplying  several 
lines  of  symbols  at  one  operation,  can  not  but 
perceive  that  in  raising  a  binomial  to  a  power, 
the  co-efficients  must  depend  on  the  laws  of  per- 
mutation and  combination  :  and  as  soon  as  this 
is  recognized,  the  theorem  is  demonstrated. 
Indeed,  when  once  it  was  seen  that  the  law  pre- 
vailed in  a  few  of  the  lower  powers,  its  identity 
with  the  law  of  permutation  would  at  once  sug- 
gest the  considerations  which  prove  it  to  obtain 
universally.  Even,  therefore,  such  cases  as 
these,  are  but  examples  of  what  I  have  called  In- 


QUOTATIONS   OK   INDUCTION.  331 

d action  by  parity  of  reasoning,  that  is,  not  really 
Induction,  because  not  involving  inference  of  a 
general  proposition  from  particular  instances. 

§  3.  There  remains  a  third  improper  use  of 
the  term  Induction,  which  it  is  of  real  impor- 
tance to  clear  up,  because  the  theory  of  Induction 
has  been,  in  no  ordinary  degree,  confused  by  it, 
and  because  the  confusion  is  exemplified  in  the 
most  recent  and  elaborate  treatise  on  the  induc- 
tive philosophy  which  exists  in  our  language. 
The  error  in  question  is  that  of  confounding  a 
mere  description,  by  general  terms,  of  a  set  of 
observed  phenomena,  with  an  induction  from 
them. 

Suppose  that  a  phenomenon  consists  of  parts, 
and  that  these  parts  are  only  capable  of  being 
observed  separately,  and  as  it  were  piecemeal. 
When  the  observations  have  been  made,  there  is 
a  convenience  (amounting  for  many  purposes  to 
a  necessity)  in  obtaining  a  representation  of  the 
phenomenon  as  a  whole,  by  combining,  or  as  we 
may  say,  piecing  these  detached  fragments  to- 
gether. A  navigator  sailing  in  the  midst  of  the 
ocean  discovers  land  :  he  can  not  at  first,  or  by  any 
one  observation,  determine  whether  it  is  a  conti- 
nent or  an  island  ;  but  he  coasts  along  it,  and 
after  a  few  days  finds  himself  to  have  sailed  com- 
pletely round  it :  he  then  pronounces  it  an  island. 
Now  there  was  no  particular  time  or  place  of  ob- 
servation at  which  he  could  perceive  that  this 
land  was  entirely  surrounded  by  water  :  he  as- 
certained the  fact  by  a  succession  of  partial  ob- 
servations, and  then  selected  a  general  expression 


332  QUOTATIONS   ON   INDUCTION. 

which  summed  up  in  two  or  three  words  the 
whole  of  what  he  so  observed.  But  is  there  any 
thing  of  the  nature  of  an  induction  in  this  pro- 
cess ?  Did  he  infer  any  thing  that  had  not  been 
observed,  from  something  else  which  had  ?  Cer- 
tainly not.  He  had  observed  the  whole  of  what 
the  proposition  asserts.  That  the  land  in  ques- 
tion is  an  island,  is  not  an  inference  from  the 
partial  facts  which  the  navigator  saw  in  the 
course  of  his  circumnavigation  ;  it  is  the  facts 
themselves  ;  it  is  a  summary  of  those  facts  ;  the 
description  of  a  complex  fact,  to  which  those 
simpler  ones  are  as  the  parts  of  a  whole. 

Now  there  is,  I  conceive,  no  difference  in  kind 
between  this  simple  operation,  and  that  by  which 
Kepler  ascertained  the  nature  of  the  planetary 
orbits  :  and  Kepler's  operation,  all  at  least  that 
was  characteristic  in  it,  was  not  more  an  induc- 
tive act  than  that  of  our  supposed  navigator. 

The  object  of  Kepler  was  to  determine  the 
real  path  described  by  each  of  the  planets,  or  let 
us  say  by  the  planet  Mars  (since  it  was  of  that 
body  that  he  first  established  the  two  of  his  three 
laws  which  did  not  require  a  comparison  of  plan- 
ets). To  do  this  there  was  no  other  mode  than 
that  of  direct  observation  :  and  all  which  obser- 
vation could  do  was  to  ascertain  a  great  number 
of  the  successive  places  of  the  planet  ;  or  rather, 
of  its  apparent  places.  That  the  planet  occupied 
successively  all  these  positions,  or  at  all  events, 
positions  which  produced  the  same  impressions 
on  the  eye,  and  that  it  passed  from  one  of  these 
to  another  insensibly,  and  without  any  apparent 


QUOTATIONS   ON   INDUCTION.  333 

breach  of  continuity  ;  thus  much  the  senses, 
with  the  aid  of  the  proper  instruments,  could 
ascertain.  What  Kepler  did  more  than  this, 
was  to  find  what  sort  of  a  curve  these  different 
points  would  make,  supposing  them  to  be  all 
joined  together.  He  expressed  the  whole  series 
of  the  observed  places  of  Mars  by  what  Dr.  Whe- 
well  calls  the  general  conception  of  an  ellipse. 
This  operation  was  far  from  being  as  easy  as 
that  of  the  navigator  who  expressed  the  series  of 
his  observations  on  successive  points  of  the 
coast  by  the  general  conception  of  an  island. 
But  it  is  the  very  same  sort  of  operation  ;  and  if 
the  one  is  not  an  induction  but  a  description, 
this  must  also  be  true  of  the  other. 

The  only  real  induction  concerned  in  the  case, 
consisted  in  inferring  that  because  the  observed 
places  of  Mars  were  correctly  represented  by 
points  in  an  imaginary  ellipse,  therefore  Mars 
would  continue  to  revolve  in  that  same  ellipse  ; 
and  in  concluding  (before  the  gap  had  been 
filled  up  by  further  observations)  that  the  posi- 
tions of  the  planet  during  the  time  which  inter- 
vened between  two  observations,  must  have  coin- 
cided with  the  intermediate  points  of  the  curve. 
For  these  were  facts  which  had  not  been  directly 
observed.  They  were  inferences  from  the  obser- 
vations ;  facts  inferred,  as  distinguished  from 
facts  seen.  But  these  inferences  were  so  far  from 
being  a  part  of  Kepler's  philosophical  operation, 
that  they  had  been  drawn  long  before  he  was 
born.  Astronomers  had  long  known  that  the 
planets  periodically  returned  to  the  same  places. 


334  QUOTATIONS   OK   INDUCTION. 

When  this  had  been  ascertained,  there  was  no 
induction  left  for  Kepler  to  make,  nor  did  he 
make  any  further  induction.  He  merely  applied 
his  new  conception  to  the  facts  inferred,  as  he 
did  to  the  facts  observed.  Knowing  already  that 
the  planets  continued  to  move  in  the  same  paths  ; 
when  he  found  that  an  ellipse  correctly  repre- 
sented the  past  path,  he  knew  that  it  would  rep- 
resent the  future  path.  In  finding  a  compen- 
dious expression  for  the  one  set  of  facts,  he 
found  one  for  the  other  :  but  he  found  the  ex- 
pression only,  not  the  inference  ;  nor  did  he 
(which  is  the  true  test  of  a  general  truth)  add 
any  thing  to  the  power  of  prediction  already 
possessed. 

§  4.  The  descriptive  operation  which  enables 
a  number  of  details  to  be  summed  up  in  a  single 
proposition,  Dr.  Whewell,  by  an  aptly  chosen 
expression,  has  termed  the  Colligation  of  Facts. 
In  most  of  his  observations  concerning  that  men- 
tal process  I  fully  agree,  and  would  gladly  trans- 
fer all  that  portion  of  his  book  into  my  own 
pages.  I  only  think  him  mistaken  in  setting  up 
this  kind  of  operation,  which  according  to  the 
old  and  received  meaning  of  the  term,  is  not  in- 
duction at  all,  as  the  type  of  induction  generally; 
and  laying  down,  throughout  his  work,  as  prin- 
ciples of  induction,  the  principles  of  mere  colli- 
gation. 

Dr.  Whewell  maintains  that  the  general  prop- 
osition which  binds  together  the  particular 
facts,  and  makes  them,  as  it  were,  one  fact,  is 
not  the  mere  sum  of  those  facts,  but  something 


QUOTATIONS   ON   INDUCTION".  335 

more,  since  there  is  introduced  a  conception  of 
the  mind,  which  did  not  exist  in  the  facts  them- 
selves. "  The  particular  facts, "  says  he,*  "  are 
not  merely  brought  together,  but  there  is  a  new  ete- 
ment  added  to  the  combination  by  the  very  act  of 
thought  by  which  they  are  combined.  .  . 
When  the  Greeks,  after  long  observing  the  mo- 
tions of  the  planets,  baw  that  these  motions 
might  be  rightly  considered  as  produced  by  the 
motion  of  one  wheel  revolving  in  the  inside  of  an- 
other wheel,  these  wheels  were  creations  of  their 
minds,  added  to  the  facts  which  they  perceived 
by  sense.  And  even  if  the  wheels  were  no 
longer  supposed  to  be  material,  but  were  reduced 
to  mere  geometrical  spheres  or  circles,  they  were 
not  the  less  products  of  the  mind  alone — some- 
thing additional  to  the  facts  observed.  The 
same  is  the  case  in  all  other  discoveries.  The 
facts  are  known,  but  they  are  insulated  and  un- 
connected, till  the  discoverer  supplies  from  his 
own  store  a  principle  of  connection.  The  pearls 
are  there,  but  they  will  not  hang  together  till 
some  one  provides  the  string. '  * 

Let  me  first  remark  that  Dr.  Whewell,  in  this 
passage,  blends  together,  indiscriminately,  ex- 
amples of  both  the  processes  which  I  am  endeav- 
oring to  distinguish  from  one  another.  When 
the  Greeks  abandoned  the  supposition  that  the 
planetary  motions  were  produced  by  the  revo- 
lution of  material  wheels,  and  fell  back  upon  the 
idea  of  u  mere  geometrical  spheres  or  circles/' 

*  Novum  Orgamim  Renovatum,  pp.  72,  73. 


336  QUOTATIONS   ON   INDUCTION. 

there  was  more  in  this  change  of  opinion  than 
the  mere  substitution  of  an  ideal  curve  for  a 
physical  one.  There  was  the  abandonment  of  a 
theory,  and  the  replacement  of  it  by  a  mere  de- 
scription. No  one  would  think  of  calling  the 
doctrine  of  material  wheels  a  mere  description. 
That  doctrine  was  an  attempt  to  point  out  the 
force  by  which  the  planets  were  acted  upon,  and 
compelled  to  move  in  their  orbits.  But  when, 
by  a  great  step  in  philosophy,  the  materiality  of 
the  wheels  was  discarded,  and  the  geometrical 
forms  alone  retained,  the  attempt  to  account  for 
the  motions  was  given  up,  and  what  was  left  of 
the  theory  was  a  mere  description  of  the  orbits. 
The  assertion  that  the  planets  were  carried  round 
by  wheels  revolving  in  the  inside  of  other 
wheels,  gave  place  to  the  proposition,  that  they 
moved  in  the  same  lines  which  would  be  traced 
by  bodies  so  carried  :  which  was  a  mere  mode 
of  representing  the  sum  of  the  observed  facts  ; 
as  Kepler's  was  another^  and  a  better  mode  of 
representing  the  same  observations. 

It  is  true  that  for  these  simply  descriptive  op- 
erations, as  well  as  for  the  erroneous  inductive 
one,  a  conception  of  the  mind  was  required. 
The  conception  of  an  ellipse  must  have  presented 
itself  to  Kepler's  mind,  before  he  could  identify 
the  planetary  orbits  with  it.  According  to  Dr. 
Whewell,  the  conception  was  something  added 
to  the  facts.  He  expresses  himself  as  if  Kepler 
had  put  something  into  the  facts  by  his  mode 
of  conceiving  them.  But  Kepler  did  no  such 
thing.  The  "ellipse  was  in  the  facts  before  Kep- 


QUOTATIONS   ON   INDUCTION.  337 

ler  recognized  it  ;  just  as  the  island  was  an  island 
before  it  had  been  sailed  round.  Kepler  did 
not  put  what  he  had  conceived  into  the  facts,  but 
saw  it  in  them.  A  conception  implies,  and  cor- 
responds to,  something  conceived  :  and  though 
the  conception  itself  is  not  in  the  facts,  but  in 
our  mind,  yet  if  it  is  to  convey  any  knowledge 
relating  to  them,  it  must  be  a  conception  of 
something  which  really  is  in  the  facts,  some  pro- 
perty which  they  actually  possess,  and  which 
they  would  manifest  to  our  senses,  if  our  senses- 
were  able  to  take  cognizance  of  it.  If,  for  in- 
stance, the  planet  left  behind  it  in  space  a  visible 
track,  and  if  the  observer  were  in  a  fixed  posi- 
tion at  such  a  distance  from  the  plane  of  the 
orbit  as  would  enable  him  to  see  the  whole  of  it 
at  once,  he  would  see  it  to  be  an  ellipse  ;  and  if 
gifted  with  appropriate  instruments  and  powers- 
of  locomotion,  he  could  prove  it  to  be  such  by 
measuring  its  different  dimensions.  Nay,  fur- 
ther :  if  the  track  were  visible,  and  he  were  so- 
placed  that  he  could  see  all  parts  of  it  in  succes- 
sion, but  not  all  of  them  at  once,  he  might  be 
able,  by  piecing  together  his  successive  observa- 
tions, to  discover  both  that  it  was  an  ellipse  and 
that  the  planet  moved  in  it.  The  case  would 
then  exactly  resemble  that  of  the  navigator  who- 
discovers  the  land  to  be  an  island  by  sailing 
round  it.  If  the  path  was  visible,  no  one  I 
think  would  dispute  that  to  identify  it  with  an 
ellipse  is  to  describe  it :  and  I  can  not  see  why 
any  difference  should  be  made  by  its  not  being 


338  QUOTATIONS   ON   INDUCTION. 

directly  an  object  of  sense,  when  every  point  in  it 
is  as  exactly  ascertained  as  if  it  were  so. 

Subject  to  the  indispensable  condition  which 
has  just  been  stated,  I  do  not  conceive  that  the 
part  which  conceptions  have  in  the  operation  of 
studying  facts,  has  ever  been  overlooked  or  un- 
dervalued. No  one  ever  disputed  that  in  order 
to  reason  about  any  thing  we  must  have  a  concep- 
tion of  it  ;  or  that  when  we  include  a  multitude 
of  things  under  a  general  expression,  there  is  im- 
plied in  the  expression  a  conception  of  something 
common  to  those  things.  But  it  by  no  means 
follows  that  the  conception  is  necessarily  pre-ex- 
istent,  or  constructed  by  the  mind  out  of  its  own 
materials.  If  the  facts  are  rightly  classed  under 
the  conception,  it  is  because  there  is  in  the  facts 
themselves  something  of  which  the  conception  is 
itself  a  copy  $  and  which  if  we  can  not  directly 
perceive,  it  is  because  of  the  limited  power  of 
our  organs,  and  not  because  the  thing  itself  is  not 
there.  The  conception  itself  is  often  obtained 
by  abstraction  from  the  very  facts  which,  in  Dr. 
WhewelPs  language,  it  is  afterward  called  in  to 
connect.  This  he  himself  admits,  when  he  ob- 
serves (which  he  does  on  several  occasions),  how 
great  a  service  would  be  rendered  to  the  science 
of  physiology  *by  the  philosopher  ' l  who  should 
establish  a  precise,  tenable,  and  consistent  con- 
ception of  life."  *  Such  a  conception  can  only 
he  abstracted  from  the  phenomena  of  life  itself  ; 
from  the  very  facts  which  it  is  put  in  requisition 

*  Jtfovum  Organum  Renovatum,  p.  32. 


QUOTATIONS   ON   INDUCTION.  339 

to  connect.  In  other  cases,  no  doubt,  instead  of 
collecting  the  conception  from  the  very  phenom- 
ena which  we  are  attempting  to  colligate,  we  se- 
lect it  from  among  those  which  have  been  pre- 
viously collected  by  abstraction  from  other  facts. 
In  the  instance  of  Kepler's  laws,  the  latter  was 
the  case.  The  facts  being  out  of  the  reach  of 
being  observed,  in  any  such  manner  as  would  have 
enabled  the  senses  to  identify  directly  the  path  of 
the  planet,  the  conception  requisite  for  framing 
a  general  description  of  that  path  could  not  be 
collected  by  abstraction  from  the  observations 
themselves  ;  the  mind  had  to  supply  hypotheti- 
cally,  from  among  the  conceptions  it  had  ob- 
tained from  other  portions  of  its  experience, 
some  one  which  would  correctly  represent  the 
series  of  the  observed  facts.  It  had  to  frame  a 
supposition  respecting  the  general  course  of  the 
phenomenon,  and  ask  itself,  If  this  be  the  general 
description,  what  will  the  details  be  ?  and  then 
compare  these  with  the  details  actually  observed. 
If  they  agreed,  the  hypothesis  would  serve  for  a 
description  of  the  phenomenon  :  if  not,  it  was 
necessarily  abandoned,  and  another  tried.  It  is 
such  a  case  as  this  which  gives  rise  to  the  doc- 
trine that  the  mind,  in  framing  the  descriptions, 
adds  something  of  its  own  which  it  does  not  find 
in  the  facts. 

Yet  it  is  a  fact  surely,  that  the  planet  does 
describe  an  ellipse  ;  and  a  fact  which  we  could 
see,  if  we  had  adequate  visual  organs  and  a  suit- 
able position.  Not  having  these  advantages,  but 
possessing  the  conception  of  an  ellipse,  or  (to  ex- 


340  QUOTATIONS   OK   INDUCTION. 

press  the  meaning  in  less  technical  language) 
knowing  what  an  ellipse  was,  Kepler  tried 
whether  the  observed  places  of  the  planet  were 
consistent  with  such  a  path.  He  found  they 
were  so  ;  and  he,  consequently,  asserted  as  a 
fact  that  the  planet  moved  in  an  ellipse.  But 
.this  fact,  which  Kepler  did  not  add  to,  but  found 
in,  the  motions  of  the  planet,  namely,  that  it 
occupied  in  succession  the  various  points  in  the 
circumference  of  a  given  ellipse,  was  the  very 
fact,  the  separate  parts  of  which  had  been  sepa- 
rately observed  ;  it  was  the  sum  of  the  different 
observations. 

Having  stated  this  fundamental  difference  be- 
tween my  opinion  and  that  of  Dr.  Whewell,  I 
must  add,  that  his  account  of  the  manner  in 
which  a  conception  is  selected,  suitable  to  ex- 
press the  facts,  appears  to  me  perfectly  just. 
The  experience  of  all  thinkers  will,  I  believe, 
testify  that  the  process  is  tentative  ;  that  it  con- 
sists of  a  succession  of  guesses  ;  many  being  re- 
jected, until  one  at  last  occurs  fit  to  be  chosen. 
We  know  from  Kepler  himself  that  before  hitting 
upon  the  "  conception"  of  an  ellipse,  he  tried 
nineteen  other  imaginary  paths,  which,  finding 
them  inconsistent  with  the  observations,  he  was 
obliged  to  reject.  But,  as  Dr.  Whewell  truly 
says,  the  successful  hypothesis,  though  a  guess, 
ought  generally  to  be  called,  not  a  lucky,  but  a 
skillful  guess.  The  guesses  which  serve  to  give 
mental  unity  and  wholeness  to  a  chaos  of 
scattered  particulars,  are  accidents  which  rarely 
occur  to  any  minds  but  those  abounding  in 


QUOTATION'S   OK   INDUCTION.  341 

knowledge  and  disciplined  in  intellectual  combi- 
nations. 

How  far  this  tentative  method,  so  indispens- 
able as  a  means  to  the  colligation  of  facts  for 
purposes  of  description,  admits  of  application  to 
Induction  itself,  and  what  functions  belong  to  it 
in  that  department,  will  be  considered  in  the 
chapter  of  the  present  Book  which  relates  to 
Hypotheses.  On  the  present  occasion  we  have 
chiefly  to  distinguish  this  process  of  Colligation 
from  Induction  properly  so  called  ;  and  that  the 
distinction  may  be  made  clearer,  it  is  well  to  ad- 
vert to  a  curious  and  interesting  remark,  which 
is  as  strikingly  true  of  the  former  operation,  as 
it  appears  to  me  unequivocally  false  of  the  latter. 

In  different  stages  of  the  progress  of  knowledge, 
philosophers  have  employed,  for  the  colligation 
of  the  same  order  of  facts,  different  conceptions. 
The  early  rude  observations  of  the  heavenly 
bodies,  in  which  minute  precision  was  neither 
attained  nor  sought,  presented  nothing  inconsist- 
ent with  the  representation  of  the  path  of  a 
planet  as  an  exact  circle,  having  the  earth  for  its 
centre.  As  observations  increased  in  accuracy, 
facts  were  disclosed  which  were  not  reconcilable 
with  this  simple  supposition  :  for  the  colligation 
of  those  additional  facts,  the  supposition  was 
varied  ;  and  varied  again  and  again  as  facts  be- 
came more  numerous  and  precise.  The  earth 
was  removed  from  the  centre  to  some  other 
point  within  the  circle  ;  the  planet  was  supposed 
to  revolve  in  a  smaller  circle  called  an  epicycle, 
round  an  imaginary  point  which  revolved  in  a 


342  QUOTATIONS   ON   INDUCTION. 

circle  round  the  earth  :  in  proportion  as  observa- 
tion elicited  fresh  facts  contradictory  to  these 
representations,  other  epicycles  and  other  eccen- 
trics were  added,  producing  additional  complica- 
tion ;  until  at  last  Kepler  swept  all  these  circles 
away,  and  substituted  the  conception  of  an  exact 
ellipse.  Even  this  is  found  not  to  represent  with 
complete  correctness  the  accurate  observations  of 
the  present  day,  which  disclose  many  slight  de- 
viations from  an  orbit  exactly  elliptical.  Now 
Dr.  Whewell  has  remarked  that  these  successive 
general  expressions,  though  apparently  so  con- 
flicting, were  all  correct  : .  they  all  answered  the 
purpose  of  colligation ;  they  all  enabled  the 
mind  to  represent  to  itself  with  facility,  and  by 
a  simultaneous  glance,  the  whole  body  of  facts 
at  the  time  ascertained  :  each  in  its  turn  served 
as  a  correct  description  of  the  phenomena,  so  far 
as  the  senses  had  up  to  that  time  taken  cogni- 
zance of  them.  If  a  necessity  afterward  arose 
for  discarding  one  of  these  general  descriptions 
of  the  planet 's  orbit,  and  framing  a  different 
imaginary  line,  by  which  to  express  the  series  of 
observed  positions,  it  was  because  a  number  of 
new  facts  had  now  been  added,  which  it  was 
necessary  to  combine  with  the  old  facts  into  one 
general  description.  But  this  did  not  affect  the 
correctness  of  the  former  expression,  considered 
as  a  general  statement  of  the  only  facts  which  it 
was  intended  to  represent.  And  so  true  is  this, 
that,  as  is  well  remarked  by  M.  Comte,  these 
ancient  generalizations,  even  the  rudest  and  most 
imperfect  of  them,  that  of  uniform  movement  in 


QUOTATIONS  OK  INDUCTION.  343 

a  circle,  are  so  far  from  being  entirely  false, 
that  they  are  even  now  habitually  employed  by 
astronomers  when  only  a  rough  approximation 
to  correctness  is  required.  "  L'astronomie  mod- 
erne,  en  detruisant  sans  re  tour  les  hypotheses 
primitives,  envisagees  comme  lois  reelles  du 
monde,  a  soigneusement  maintenu  leur  valeur 
positive  et  permanente,  la  propriete  de  repre- 
senter  commodement  les  phenomenes  quand  il 
s'agit  d'une  premiere  ebauche.  Nos  ressources  a 
cet  egard  sont  me  me  bien  plus  etendues,  precise- 
ment  a  cause  que  nous  ne  nous  faisons  aucune 
illusion  sur  la  realite  des  hypotheses  ;  ce  qui 
nous  permet  d7 employer  sans  scrupule,  en  chaque 
cas,  celle  que  nous  jugeons  la  plus  avantageuse.  "* 

Dr.  Whe well's  remark,  therefore,  is  philo- 
sophically correct.  Successive  expressions  for 
the  colligation  of  observed  facts,  or,  in  other 
words,  successive  descriptions  of  a  phenomenon 
as  a  whole,  which  has  been  observed  only  in 
parts,  may,  though  conflicting,  be  all  correct  as 
far  as  they  go.  But  it  would  surely  be  absurd 
to  assert  this  of  conflicting  inductions. 

The  scientific  study  of  facts  may  be  under- 
taken for  three  different  purposes  :  the  simple 
description  of  the  facts  ;  their  explanation  ;  or 
their  prediction  :  meaning  by  prediction,  the  de- 
termination of  the  conditions  under  which  sim- 
ilar facts  may  be  expected  again  to  occur.  To 
the  first  of  these  three  operations  the  name  of 
Induction  does  not  properly  belong :  to  the 

*  Cours  de  Philosophic  Positive,  vol.  ii. ,  p.  202. 


344  QUOTATIONS   OK   INDUCTION. 

other  two  it  does.  Now,  Dr.  Whe well's  obser- 
vation is  true  of  the  first  alone.  Considered  as 
a  mere  description,  the  circular  theory  of  the 
heavenly  motions  represents  perfectly  well  their 
general  features  :  and  by  adding  epicycles  with- 
out limit,  those  motions,  even  as  now  known  to 
us,  might  be  expressed  with  any  degree  of  accu- 
racy that  might  be  required.  The  elliptical 
theory,  as  a  mere  description,  would  have  a  great 
advantage  in  point  of  simplicity,  and  in  the  con- 
sequent facility  of  conceiving  it  and  reasoning 
about  it ;  but  it  would  not  really  be  more  true 
than  the  other.  Different  descriptions,  there- 
fore, may  be  all  true  :  but  not,  surely,  different 
explanations.  The  doctrine  that  the  heavenly 
bodies  moved  by  a  virtue  inherent  in  their  celes- 
tial nature  ;  the  doctrine  that  they  were  moved 
l>y  impact  (which  led  to  the  hypothesis  of  vor- 
tices as  the  only  impelling  force  capable  of 
whirling  bodies  in  circles),  and  the  Newtonian 
doctrine,  that  they  are  moved  by  the  composi- 
tion of  a  centripetal  with  an  original  projectile 
force  ;  all  these  are  explanations,  collected  by 
real  induction  from  supposed  parallel  cases  ;  and 
they  were  all  successively  received  by  philoso- 
phers, as  scientific  truths  on  the  subject  of  the 
heavenly  bodies.  Can  it  be  said  of  these,  as 
was  said  of  the  different  descriptions,  that  they 
are  all  true  as  far  as  they  go  ?  Is  it  not  clear 
that  only  one  can  be  true  in  any  degree,  and 
the  other  two  must  be  altogether  false  ?  So 
much  for  explanations  :  let  us  now  compare 
different  predictions  :  the  first,  that  eclipses  will 


QUOTATIONS   ON   INDUCTION.  345 

occur  when  one  planet  or  satellite  is  so  situated 
as  to  cast  its  shadow  upon  another  ;  the  second, 
that  they  will  occur  when  some  great  calamity  is 
impending  over  mankind.  Do  these  two  doc- 
trines only  differ  in  the  degree  of  their  truth,  as 
expressing  real  facts  with  unequal  degrees  of  ac- 
curacy ?  Assuredly  the  one  is  true,  and  the 
other  absolutely  false.* 

*  Dr.  Whewell,  in  his  reply,  contests  the  distinction 
here  drawn,  and  maintains,  that  not  only  different 
descriptions,  but  different  explanations  of  a  phenom- 
enon, may  all  be  true.  Of  the  three  theories  respect- 
ing the  motions  of  the  heavenly  bodies,  he  says  (Phi- 
losophy of  Discovery,  p.  231)  :  "  Undoubtedly,  all  these 
explanations  may  be  true  and  consistent  with  each 
other,  and  would  be  so  if  each  had  been  followed  out 
so  as  to  show  in  what  manner  it  could  be  made  con- 
sistent with  the  facts.  And  this  was,  in  reality,  in  a 
great  measure  done.  The  doctrine  that  the  heavenly- 
bodies  were  moved  by  vortices  was  successfully  mod- 
ified, so  that  it  came  to  coincide  in  its  results  with 
the  doctrine  of  an  inverse-quadratic  centripetal  force. 
.  .  .  When  this  point  was  reached,  the  vortex  was 
merely  a  machinery,  well  or  ill  devised,  for  produc- 
ing such  a  centripetal  force,  and  therefore  did  not  con- 
tradict the  doctrine  of  a  centripetal  force.  Newton 
himself  does  not  appear  to  have  been  averse  to  ex- 
plaining gravity  by  impulse.  So  little  is  it  true  that 
if  one  theory  be  true  the  other  must  be  false.  The 
attempt  to  explain  gravity  by  the  impulse  of  streams 
of  particles  flowing  through  the  universe  in  all  direc- 
tions, which  I  have  mentioned  in  the  Philosophy,  is  so 
far  from  being  consistent  with  the  Newtonian  theory, 
that  it  is  founded  entirely  upon  it.  And  even  with 
regard  to  the  doctrine,  that  the  heavenly  bodies  move 
by  an  inherent  virtue  ;  if  this  doctrine  had  been  main- 
tained in  any  such  way  that  it  wyas  brought  to  agree 


346  QUOTATIONS   ON   INDUCTION. 

In  every  way,  therefore,  it  is  evident  that  to 
explain  induction  as  the  colligation  of  facts  by 

with  the  facts,  the  inherent  virtue  must  have  had  its 
laws  determined  ;  and  then  it  would  have  been  found 
that  the  virtue  had  a  reference  to  the  central  body  ; 
and  so,  the  '  inherent  virtue  '  must  have  coincided  in 
its  effect  with  the  Newtonian  force  ;  and  then,  the  two 
explanations  would  agree,  except  so  far  as  the  word 
'  inherent '  was  concerned.  And  if  such  a  part  of  an 
earlier  theory  as  this  word  inherent  indicates,  is  found 
to  be  untenable,  it  is  of  course  rejected  in  the  transi- 
tion to  later  and  more  exact  theories,  in  Inductions 
of  this  kind,  as  well  as  in  what  Mr.  Mill  calls  De- 
scriptions. There  is,  therefore,  still  no  validity  dis- 
coverable in  the  distinction  which  Mr.  Mill  attempts  to 
draw  between  descriptions  like  Kepler's  law  of  ellip- 
tical orbits,  and  other  examples  of  induction. ' ' 

If  the  doctrine  of  vortices  had  meant,  not  that  vor- 
tices, existed  but  only  that  the  planets  moved  in  the 
same  manner  as  if  they  had  been  whirled  by  vortices  ; 
if  the  hypothesis  had  been  merely  a  mode  of  repre- 
senting the  facts,  not  an  attempt  to  account  for  them  ; 
if,  in  short,  it  had  been  only  a  Description  ;  it  would, 
no  doubt,  have  been  reconcilable  with  the  Newtonian 
theory.  The  vortices,  however,  were  not  a  mere  aid 
to  conceiving  the  motions  of  the  planets,  but  a  sup- 
posed physical  agent,  actively  impelling  them  ;  a 
.  material  fact,  which  might  be  true  or  not  true,  but 
could  not  be  both  true  and  not  true.  According  to 
Descartes's  theory  it  was  true,  according  to  Newton's 
it  was  not  true.  Dr.  Whewell  probably  means  that 
since  the  phrases,  centripetal  and  projectile  force,  do 
not  declare  the  nature  but  only  the  direction  of  the 
forces,  the  Newtonian  theory  does  not  absolutely 
contradict  any  hypothesis  which  may  be  framed  re- 
specting the  mode  of  their  production.  The  New- 
tonian theory,  regarded  as  a  mere  description  of  the 
planetary  motions,  does  not ;  but  the  Newtonian 
theory  as  an  explanation  of  them  does.  For  in  what 


QUOTATIONS   ON   INDUCTION.  347 

means  of  appropriate  conceptions,  that  is,  con- 
ceptions which  will  really  express  them,  is  to 

does  the  explanation  consist?  In  ascribing  those 
motions  to  a  general  law  which  obtains  between  all 
particles  of  matter,  and  in  identifying  this  with  the 
law  by  which  bodies  fall  to  the  ground.  If  the 
planets  are  kept  in  their  orbits  by  a  force  which 
draws  the  particles  composing  them  toward  every 
other  particle  of  matter  in  the  solar  system,  they  are 
not  kept  in  those  orbits  by  the  impulsive  force  of 
certain  streams  of  matter  which  whirl  them  round. 
The  one  explanation  absolutely  excludes  the  other. 
Either  the  planets  are  not  moved  by  vortices,  or  they 
do  not  move  by  a  law  common  to  all  matter.  It  is 
impossible  that  both  opinions  can  be  true.  As  well 
might  it  be  said  that  there  is  no  contradiction  be- 
tween the  assertions,  that  a  man  died  because  some- 
body killed  him,  and  that  he  died  a  natural  death. 

So,  again,  the  theory  that  the  planets  move  by  a 
virtue  inherent  in  their  celestial  nature,  is  incom- 
patible wTith  either  of  the  two  others  :  either  that  of 
their  being  moved  by  vortices,  or  that  which  regards 
them  as  moving  by  a  property  which  they  have  in 
common  with  the  earth  and  all  terrestrial  bodies. 
Dr.  Whewell  says  that  the  theory  of  an  inherent 
virtue  agrees  with  Newton's  when  the  word  inherent 
is  left  out,  which  of  course  it  would  be  (he  says)  if 
"found  to  be  untenable."  But  leave  that  out,  and 
where  is  the  theory?  The  word  inherent  is  the 
theory.  When  that  is  omitted,  there  remains  nothing 
except  that  the  heavenly  bodies  move  "  by  a  virtue," 
i.e.,  by  a  power  of  some  sort ;  or  by  virtue  of  their 
celestial  nature,  which  directly  contradicts  the  doc- 
trine that  terrestrial  bodies  fall  by  the  same  law. 

If  Dr.  "Whewell  is  not  yet  satisfied,  any  other  sub- 
ject will  serve  equally  well  to  test  his  doctrine.  He 
will  hardly  say  that  there  is  no  contradiction  between 
the  emission  theory  and  the  undulatory  theory  of 
light  ;  or  that  there  can  be  both  one  and  two  electric- 


348  QUOTATIONS   ON   INDUCTION. 

confound  mere  description  of  the  observed  facts 
with  inference  from  those  facts,  and  ascribe  to 

ities  ;  or  that  the  hypothesis  of  the  production  of  the 
higher  organic  forms  by  development  from  the  lower, 
and  the  supposition  of  separate  and  successive  acts  of 
creation,  are  quite  reconcilable  ;  or  that  the  theory 
that  volcanoes  are  fed  from  a  central  fire,  and  the 
doctrines  which  ascribe  them  to  chemical  action  at  a 
comparatively  small  depth  below  the  earth's  surface, 
are  consistent  with  one  another,  and  all  true  as  far  as 
they  go. 

If  different  explanations  of  the  same  fact  can  not 
both  be  true,  still  less,  surely,  can  different  predic- 
tions. Dr.  Whewell  quarrels  (on  what  ground  it  is 
not  necessary  here  to  consider)  with  the  example  I 
had  chosen  on  this  point,  and  thinks  an  objection  to 
an  illustration  a  sufficient  answer  to  a  theory.  Ex- 
amples not  liable  to  his  objection  are  easily  found, 
if  the  proposition  that  conflicting  predictions  can  not 
both  be  true,  can  be  made  clearer  by  any  examples. 
Suppose  the  phenomenon  to  be  a  newly-discovered 
comet,  and  that  one  astronomer  predicts  its  return 
once  in  every  300  years — another  once  in  every  400  : 
can  they  both  be  right  ?  When  Columbus  predicted 
that  by  sailing  constantly  westward  he  should  in 
time  return  to  the  point  from  which  he  set  out,  while 
others  asserted  that  he  could  never  do  so  except  by 
turning  back,  were  both  he  and  his  opponents  true 
prophets  ?  Were  the  predictions  which  foretold  the 
wonders  of  railways  and  steamships,  and  those  which 
averred  that  the  Atlantic  could  never  be  crossed  by 
steam  navigation,  nor  a  railway  train  propelled  ten 
miles  an  hour,  both  (in  Dr.  Whewell's  words)  "  true, 
and  consistent  with  one  another  ?" 

Dr.  Whewell  sees  no  distinction  between  holding 
contradictory  opinions  on  a  question  of  fact,  and 
merely  employing  different  analogies  to  facilitate  the 
conception  of  the  same  fact.  The  case  of  different 
Inductions  belongs  to  the  former  class,  that  of  differ- 
ent Descriptions  to  the  latter. 


QUOTATIONS   OX   INDUCTION.  349 

the  latter  what  is  a  characteristic  property  of  the 
former. 

There  is,  however,  between  Colligation  and 
Induction,  a  real  correlation,  which  it  is  impor- 
tant to  conceive  correctly.  Colligation  is  not 
always  induction  ;  but  induction  is  always  colli- 
gation. The  assertion  that  the  planets  move  in 
ellipses,  was  but  a  mode  of  representing  observed 
facts  ;  it  was  but  a  colligation  ;  while  the  asser- 
tion that  they  are  drawn,  or  tend,  toward  the 
sun,  was  the  statement  of  a  new  fact,  inferred 
by  induction.  But  the  induction,  once  made, 
accomplishes  the  purposes  of  colligation  likewise. 
It  brings  the  same  facts,  which  Kepler  had  con- 
nected by  his  conception  of  an  ellipse,  under  the 
additional  conception  of  bodies  acted  upon  by  a 
central  force,  and  serves,  therefore,  as  a  new 
bond  of  connection  for  those  facts  ;  a  new  prin- 
ciple for  their  classification. 

Further,  the  descriptions  which  are  improp- 
erly confounded  with  induction,  are  nevertheless 
a  necessary  preparation  for  induction  ;  no  less 
necessary  than  correct  observation  of  the  facts 
themselves.  Without  the  previous  colligation  of 
detached  observations  by  means  of  one  general 
conception,  we  could  never  have  obtained  any 
basis  for  an  induction,  except  in  the  case  of 
phenomena  of  very  limited  compass.  We  should 
not  be  able  to  affirm  any  predicates  at  all,  of  a 
subject  incapable  of  being  observed  otherwise 
than  piecemeal  :  much  less  could  we  extend  those 
predicates  by  induction  to  other  similar  subjects. 
Induction,  therefore,  always  presupposes,  not 


350  QUOTATIONS   OK   INDUCTION. 

only  that  the  necessary  observations  are  made 
with  the  necessary  accuracy,  but  also  that  the 
results  of  these  observations  are,  so  far  as  prac- 
ticable, connected  together  by  general  descrip- 
tions, enabling  the  mind  to  represent  to  itself 
as  wholes  whatever  phenomena  are  capable  of 
being  so  represented. 

§  5.  Dr.  Whewell  has  replied  at  some  length 
to  the  preceding  observations,  restating  his  opin- 
ions, but  without  (as  far  as  I  can  perceive)  add- 
ing any  thing  material  to  his  former  arguments. 
Since,  however,  mine  have  not  had  the  good  for- 
tune to  make  any  impression  upon  him,  I  will 
subjoin  a  few  remarks,  tending  to  show  more 
clearly  in  what  our  difference  of  opinion  consists, 
as  well  as,  in  some  measure,  to  account  for  it. 

Nearly  all  the  definitions  of  induction,  by 
writers  of  authority,  make  it  consist  in  drawing 
inferences  from  known  cases  to  unknown  ; 
affirming  of  a  class,  a  predicate  which  has  been 
found  true  of  some  cases  belonging  to  the  class  ; 
concluding  because  some  things  have  a  certain 
property,  that  other  things  which  resemble  them 
have  the  same  property — or  because  a  thing  has 
manifested  a  property  at  a  certain  time,  that  it 
has  and  will  have  that  property  at  other  times. 

It  will  scarcely  be  contended  that  -Kepler's 
operation  was  an  Induction  in  this  sense  of  the 
term.  The  statement,  that  Mars  moves  in  an 
elliptical  orbit,  was  no  generalization  from  indi- 
vidual cases  to  a  class  of  cases.  Neither  was  it 
an  extension  to  all  time,  of  what  had  been  found 
true  at  some  particular  time.  The  whole  amount 


QUOTATIONS   ON   INDUCTIQN.  351 

of  generalization  which  the  case  admitted  of, 
was  already  completed,  or  might  have  been  so. 
Long  before  the  elliptic  theory  was  thought  of, 
it  had  been  ascertained  that  the  planets  returned 
periodically  to  the  same  apparent  places  ;  the 
series  of  these  places  was,  or  might  have  been, 
completely  determined,  and  the  apparent  course 
of  each  planet  marked  out  on  the  celestial  globe 
in  an  uninterrupted  line.  Kepler  did  not  extend 
an  observed  truth  to  other  cases  than  those  in 
which  it  had  been  observed  :  he  did  not  widen 
the  subject  of  the  proposition  which  expressed 
the  observed  facts.  The  alteration  he  made  was 
in  the  predicate.  Instead  of  saying,  the  suc- 
cessive places  of  Mars  are  so  and  so,  he  summed 
them  up  in  the  statement,  that  the  successive 
places  of  Mars  are  points  in  an  ellipse.  It  is 
true,  this  statement,  as  Dr.  Whewell  says,  was 
not  the  sum  of  the  observations  merely ;  it  was 
the  sum  of  the  observations  seen  under  a  new  point 
of  view.  *  But  it  was  not  the  sum  of  more  than 
the  observations,  as  a  real  induction  is.  It  took 
in  no  cases  but  those  which  had  been  actually  ob- 
served, or  which  could  have  been  inferred  from 
the  observations  before  the  new  point  of  view 
presented  itself.  There  was  not  that  transition 
from  known  cases  to  unknown,  which  constitutes 
Induction  in  the  original  and  acknowledged 
meaning  of  the  term. 

Old    definitions,  it    is  true,  can    not    prevail 
against  new  knowledge  :    and  if  the  Keplerian 

*  Phil  ofDiscov.,?.  256. 


352  QUOTATIONS   ON   INDUCTION. 

• 

operation,  as  a  logical  process,  be  really  identical 
with  what  takes  place  in  acknowledged  induc- 
tion, the  definition  of  induction  ought  to  be  so 
widened  as  to  take  it  in  ;  since  scientific  language 
ought  to  adapt  itself  to  the  true  relations  which 
subsist  between  the  things  it  is  employed  to  des- 
ignate. Here  then  it  is  that  I  am  at  issue  with 
Dr.  Whewell.  He  does  think  the  operations 
identical.  He  allows  of  no  logical  process  in 
any  case  of  induction,  other  than  what  there  was 
in  Kepler's  case,  namely,  guessing  until  a  guess 
is  found  which  tallies  with  the  facts  ;  and  ac- 
cordingly, as  we  shall  see  hereafter,  he  rejects  all 
canons  of  induction,  because  it  is  not  by  means 
of  them  that  we  guess.  Dr.  Whewell' s  theory 
of  the  logic  of  science  would  be  very  perfect  if 
it  did  not  pass  over  altogether  the  question  of 
Proof.  But  in  my  apprehension  there  is  such  a 
thing  as  proof,  and  inductions  differ  altogether 
from  descriptions  in  their  relation  to  that  ele- 
ment. Induction  is  proof  ;  it  is  inferring  some- 
thing unobserved  from  something  observed  :  it 
requires,  therefore,  an  appropriate  test  of  proof  ; 
and  to  provide  that  test,  is  the  special  purpose 
of  inductive  logic.  When,  on  the  contrary,  we 
merely  collate  known  observations,  and,  in  Dr. 
Whew  ell's  phraseology,  connect  them  by  means 
of  a  new  conception  ;  if  the  conception  does 
serve  to  connect  the  observations,  we  have  all 
we  want.  As  the  proposition  in  which  it  is  em- 
bodied pretends  to  no  other  truth  than  what  it 
may  share  with  many  other  modes  of  represent- 
ing the  same  facts,  to  be  consistent  with  the  facts 


QUOTATIONS   OK   INDUCTION.  353 

is  all  it  requires  :  it  neither  needs  nor  admits 
of  proof  ;  though  it  may  serve  to  prove  other 
things,  inasmuch  as,  by  placing  the  facts  in 
mental  connection  with  other  facts,  not  previ- 
ously seen  to  resemble  them,  it  assimilates  the 
case  to  another  class  of  phenomena,  concerning 
which  real  Inductions  have  already  been  made. 
Thus  Kepler's  so-called  law  brought  the  orbit  of 
Mars  into  the  class  ellipse,  and  by  doing  so, 
proved  all  the  properties  of  an  ellipse  to  be  true 
of  the  orbit :  but  in  this  proof  Kepler's  law  sup- 
plied the  minor  premise,  and  not  (as  is  the  case 
with  real  Inductions)  the  major. 

Dr.  Whewell  calls  nothing  Induction  where 
there  is  not  a  new  mental  conception  introduced, 
and  every  thing  induction  where  there  is.  But 
this  is  to  confound  two  very  different  things,  In- 
vention and  Proof.  The  introduction  of  a  new 
conception  belongs  to  Invention  :  and  invention 
may  be  required  in  any  operation,  but  is  the  es- 
sence of  none.  A  new  conception  may  be  intro- 
duced for  descriptive  purposes,  and  so  it  may  for 
inductive  purposes.  But  it  is  so  far  from  con- 
stituting induction,  that  induction  does  not  nec- 
essarily stand  in  need  of  it.  Most  inductions 
require  no  conception  but  what  was  present  in 
every  one  of  the  particular  instances  on  which 
the  induction  is  grounded.  That  all  men  are 
mortal  is  surely  an  inductive  conclusion  ;  yet  no 
new  conception  is  introduced  by  it.  Whoever 
knows  that  any  man  has  died,  has  all  the  concep- 
tions involved  in  the  inductive  generalization.  But 
Dr.  Whewell  considers  the  process  of  invention 


354  QUOTATIONS   OX   INDUCTION. 

which  consists  in  framing  a  new  conception  con- 
sistent with  the  facts,  to  be  not  merely  a  neces- 
sary part  of  all  induction,  but  the  whole  of  it. 

The  mental  operation  which  extracts  from  a 
number  of  detached  observations  certain  general 
characters  in  which  the  observed  phenomena  re- 
semble one  another,  or  resemble  other  known 
facts,  is  what  Bacon,  Locke,  and  most  subse- 
quent metaphysicians,  have  understood  by  the 
word  Abstraction.  A  general  expression  ob- 
tained by  abstraction,  connecting  known  facts 
by  means  of  common  characters,  but  without 
concluding  from  them  to  unknown,  may,  I 
think,  with  strict  logical  correctness,  be  termed 
a  Description  ;  nor  do  I  know  in  what  other  way 
things  can  ever  be  described.  My  position,  how- 
€ver,  does  not  depend  on  the  employment  of  that 
particular  word  ;  I  am  quite  content  to  use  Dr. 
WhewelPs  term  Colligation,  or  the  more  gen- 
eral phrases,  '  mode  of  representing,  or  of  ex- 
pressing, phenomena  : '  provided  it  be  clearly 
seen  that  the  process  is  not  Induction,  but 
something  radically  different. 

What  more  may  usefully  be  said  on  the  subject 
-of  Colligation,  or  of  the  correlative  expression 
invented  by  Dr.  Whewell,  the  Explication  of 
Conceptions,  and  generally  on  the  subject  of 
ideas  and  mental  representations  as  connected 
with  the  study  of  facts,  will  find  a  more  appro- 
priate place  in  the  Fourth  Book,  on  the  Opera- 
tions Subsidiary  to  Induction  :  to  which  I  must 
refer  the  reader  for  the  removal  of  any  difficulty 
"which  the  present  discussion  may  have  left. 


QUOTATIONS   ON   INDUCTION.  355 


OF    THE    GROUND    OF    INDUCTION. 

§  1.  INDUCTION  properly  so  called,  as  dis- 
tinguished from  those  mental  operations,  some- 
times, though  improperly,  designated  by  the 
name,  which  I  have  attempted  in  the  preceding 
chapter  to  characterize,  may,  then,  be  summarily 
defined  as  Generalization  from  Experience.  It 
consists  in  inferring  from  some  individual  in- 
stances in  which  a  phenomenon  is  observed  to 
occur,  that  it  occurs  in  all  instances  of  a  certain 
class  ;  namely,  in  all  which  resemble  the  former, 
in  what  are  regarded  as  the  material  circum- 
stances. 

In  what  way  the  material  circumstances  are 
to  be  distinguished  from  those  which  are  imma- 
terial, or  why  some  of  the  circumstances  are  ma- 
terial and  others  not  so,  we  are  not  yet  ready  to 
point  out.  We  must  first  observe,  that  there  is 
a  principle  implied  in  the  very  statement  of  what 
Induction  is  ;  an  assumption  with  regard  to  the 
course  of  nature  and  the  order  of  the  universe  ; 
namely,  that  there  are  such  things  in  nature  as 
parallel  cases  ;  that  what  happens  once,  will, 
under  a  sufficient  degree  of  similarity  of  circum- 
stances, happen  again,  and  not  only  again,  but 
as  often  as  the  same  circumstances  recur.  This, 
I  say,  is  an  assumption,  involved  in  every  case 
of  induction.  And,  if  we  consult  the  actual 
course  of  nature,  we  find  that  the  assumption  is 
warranted.  The  universe,  so  far  as  known  to 
us,  is  so  constituted,  that  whatever  is  true  in 
any  one  case,  is  true  in  all  cases  of  a  certain  de- 


356  QUOTATIONS   ON   INDUCTION. 

script! on  ;  the  only  difficulty  is,  to  find  what  de- 
scription. 

This  universal  fact,  which  is  our  warrant  for 
all  inferences  from  experience,  has  been  de- 
scribed by  different  philosophers  in  different 
forms  of  language  :  that  the  course  of  nature  is 
uniform  ;  that  the  universe  is  governed  by  gen- 
eral laws  ;  and  the  like.  One  of  the  most  usual 
of  these  modes  of  expression,  but  also  one  of 
the  most  inadequate,  is  that  which  has  been 
brought  into  familiar  use  by  the  metaphysicians 
of  the  school  of  Reid  and  Stewart.  The  dispo- 
sition of  the  human  mind  to  generalize  from  ex- 
perience— a  propensity  considered  by  these  phi- 
losophers as  an  instinct  of  our  nature — they  usu- 
ally describe  under  some  such  name  as  "  our  in- 
tuitive conviction  that  the  future  will  resemble 
the  past."  Now  it  has  been  well  pointed  out  by 
Mr.  Bailey,*  that  (whether  the  tendency  be  or 
not  an  original  and  ultimate  element  of  our  na- 
ture), Time,  in  its  modifications  of  past,  present, 
and  future,  has  no  concern  either  with  the  belief 
itself,  or  with  the  grounds  of  it.  We  believe 
that  fire  will  burn  to-morrow,  because  it  burned 
to-day  and  yesterday  ;  but  we  believe,  on  pre- 
cisely the  same  grounds,  that  it  burned  before  we 
were  born,  and  that  it  burns  this  very  day  in 
Cochin-China.  It  is  not  from  the  past  to  the 
future,  as  past  and  future,  that  we  infer,  but  from 
the  known  to  the  unknown  ;  from  facts  observed 
to  facts  unobserved  ;  from  what  we  have  per- 

*  Essays  an  tJie  Pursuit  of  Truth. 


QUOTATIONS   ON   INDUCTION.  357 

ceived,  or  been  directly  conscious  of,  to  what  has 
not  come  within  onr  experience.  In  this  last 
predicament  is  the  whole  region  of  the  future  ; 
but  also  the  vastly  greater  portion  of  the  present 
and  of  the  past. 

Whatever  be  the  most  proper  mode  of  express- 
ing it,  the  proposition  that  the  course  of  nature 
is  uniform,  is  the  fundamental  principle,  or  gen- 
eral axiom,  of  Induction.  It  would  yet  be  a 
great  error  to  offer  this  large  generalization  as 
any  explanation  of  the  inductive  process.  On  the 
contrary,  I  hold  it  to  be  itself  an  instance  of  in- 
duction, and  induction  by  no  means  of  the  most 
obvious  kind.  Far  from  being  the  first  induction 
we  make,  it  is  one  of  the  last,  or  at  all  events  one 
of  those  which  are  latest  in  attaining  strict  phil- 
osophical accuracy.  As  a  general  maxim,  indeed, 
it  has  scarcely  entered  into  the  minds  of  any  but 
philosophers;  nor  even  by  them,  as  we  shall  have 
many  opportunities  of  remarking,  have  its  extent 
and  limits  been  always  very  justly  conceived. 
The  truth  is,  that  this  great  generalization  is  itself 
founded  on  prior  generalizations.  The  obscurer 
laws  of  nature  were  discovered  by  means  of  it, 
but  the  more  obvious  ones  must  have  been  under- 
stood and  assented  to  as  general  truths  before  it 
was  ever  heard  of.  We  should  never  have  thought 
of  affirming  that  all  phenomena  take  place  ac- 
cording to  general  laws,  if  we  had  not  first  arrived, 
in  the  case  of  a  great  multitude  of  phenomena, 
at  some  knowledge  of  the  laws  themselves  ;  which 
could  be  done  no  otherwise  than  by  induction. 
In  what  sense,  then,  can  a  principle,  which  is  so 


358  QUOTATIONS   OK   INDUCTION. 

far  from  being  our  earliest  induction,  be  regarded 
as  our  warrant  for  all  the  others  ?  In  the  only 
sense,  in  which  (as  we  have  already  seen)  the 
general  propositions  which  we  place  at  the  head 
of  our  reasonings  when  we  throw  them  into  syl- 
logisms, ever  really  contribute  to  their  validity. 
As  Archbishop  Whately  remarks,  every  induction 
is  a  syllogism  with  the  major  premise  suppress- 
ed ;  or  (as  I  prefer  expressing  it)  every  induction 
may  be  thrown  into  the  form  of  a  syllogism,  by 
supplying  a  major  premise.  If  this  be  actually 
done,  the  principle  which  we  are  now  considering, 
that  of  the  uniformity  of  the  course  of  nature, 
will  appear  as  the  ultimate  major  premise  of  all 
inductions,  and  will,  therefore,  stand  to  all  in- 
ductions in  the  relation  in  which,  as  has  been 
shown  at  so  much  length,  the  major  proposition 
of  a  syllogism  always  stands  to  the  conclusion  ; 
not  contributing  at  all  to  prove  it,  but  being  a 
necessary  condition  of  its  being  proved  ;  since  no 
conclusion  is  proved,  for  which  there  can  not  be 
found  a  true  major  premise.* 

*  In  the  first  edition  a  note  was  appended  at  this 
place,  containing  some  criticism  on  Archbishop's 
Whately 's  mode  of  conceiving  the  relation  between 
Syllogism  and  Induction.  In  a  subsequent  issue  of 
his  Logic,  the  Archbishop  made  a  reply  to  the  criti- 
cism, which  induced  me  to  cancel  part  of  the  note, 
incorporating  the  remainder  in  the  text.  In  a  still 
later  edition,  the  Archbishop  observes  in  a  tone  of 
something  like  disapprobation,  that  the  objections, 
*'  doubtless  from  their  being  fully  answered  and 
found  untenable,  were  silently  suppressed,"  and  that 
hence  he  might  appear  to  some  of  his  readers  to  be 


QUOTATIONS   ON   INDUCTION".  359 

The  statement,  that  the  uniformity  of  the  course 
of  nature  is  the  ultimate  major  premise  in  all  cases 


combating  a  shadow.  On  this  latter  point,  the  Arch- 
bishop need  give  himself  no  uneasiness.  His  readers, 
I  make  bold  to  say,  will  fully  credit  his  mere  affirm- 
ation that  the  objections  have  actually  been  made. 

But  as  he  seems  to  think  that  what  he  terms  the 
suppression  of  the  objections  ought  not  to  have  been 
made  "  silently,"  I  now  break  that  silence,  and 
state  exactly  what  it  is  that  I  suppressed,  and  why. 
I  suppressed  that  alone  which  might  be  regarded  as 
personal  criticism  on  the  Archbishop.  I  had  imput- 
ed to  him  the  having  omitted  to  ask  himself  a  partic- 
ular question.  I  found  that  he  had  asked  himself  the 
question,  and  could  give  it  an  answer  consistent  with 
his  own  theory.  I  had  also,  within  the  compass  of  a 
parenthesis,  hazarded  some  remarks  on  certain  general 
characteristics  of  Archbishop  Whately  as  a  philoso- 
pher. These  remarks,  though  their  tone,  I  hope,  was 
neither  disrespectful  nor  arrogant,  I  felt,  on  recon- 
sideration, that  I  was  hardly  entitled  to  make  ;  least 
of  all,  when  the  instance  which  I  had  regarded  as  an 
illustration  of  them,  failed,  as  I  now  saw,  to  bear 
them  out.  The  real  matter  at  the  bottom  of  the 
whole  dispute,  the  different  view  we  take  of  the 
function  of  the  major  premise,  remains  exactly  where 
it  was  ;  and  so  far  was  I  from  thinking  that  my 
opinion  had  been  fully  "  answered"  and  was  "un- 
tenable," that  in  the  same  edition  in  which  I  can- 
celled the  note,  I  not  only  enforced  the  opinion  by 
further  arguments,  but  answered  (though  without 
naming  him)  those  of  the  Archbishop. 

For  not  having  made  this  statement  before,  I  do 
not  think  it  needful  to  apologize.  It  would  be  at- 
taching very  great  importance  to  one's  smallest  say- 
ings, to  think  a  formal  retractation  requisite  every 
time  that  one  falls  into  an  error.  Nor  is  Archbishop 
"Whately 's  well-earned  fame  of  so  lender  a  quality  as 


360  QUOTATIONS   ON   INDUCTION. 

of  induction,  may  be  thought  to  require  some 
explanation.  The  immediate  major  premise  in 
every  inductive  argument,  it  certainly  is  not.  Of 
that,  Archbishop  Whately 's  must  be  held  to  be  the 
correct  account.  The  induction,  "  John,  Peter, 
etc.,  are  mortal,  therefore  all  mankind  are  mor- 
tal," may,  as  he  justly  says,  be  thrown  into  a  syl- 
logism by  prefixing  as  a  major  premise  (what  is  at 
any  rate  a  necessary  condition  of  the  validity  of 
the  argument),  namely,  that  what  is  true  of  John 
Peter,  etc.,  is  true  of  all  mankind.  But  how 
came  we  by  this  major  premise  ?  It  is  not  self- 
evident  ;  nay,  in  all  cases  of  unwarranted  gene- 
ralization, it  is  not  true.  How,  then,  is  it  arrived 
at  ?  Necessarily  either  by  induction  or  ratioci- 
nation ;  and  if  by  induction,  the  process,  like  all 
other  inductive  arguments,  may  be  thrown  into 
the  form  of  a  syllogism.  This  previous  syllogism 
it  is,  therefore,  necessary  to  construct.  There  is, 
in  the  long  run,  only  one  possible  construction. 
The  real  proof  that  what  is  true  of  John,  Peter, 
etc.,  is  true  of  all  mankind,  can  only  be,  that  a 
different  supposition  would  be  inconsistent  with 
the  uniformity  which  we  know  to  exist  in  the 
course  of  nature.  Whether  there  would  be  this 
inconsistency  or  not,  may  be  a  matter  of  long  and 
delicate  inquiry  ;  but  unless  there  would,  we  have 
no  sufficient  ground  for  the  major  of  the  induct- 
ive syllogism.  It  hence  appears,  that  if  we  throw 
the  whole  course  of  any  inductive  argument  into 

to  require  that  in  withdrawing  a  slight  criticism  on 
him  I  should  have  been  bound  to  offer  a  public 
amende  for  having  made  it. 


QUOTATIONS   ON   INDUCTION.  361 

a  series  of  syllogisms,  we  shall  arrive  by  more  or 
fewer  steps  at  an  ultimate  syllogism,  which  will 
have  for  its  major  premise  the  principle,  or  axi- 
om, of  the  uniformity  of  the  course  of  nature.* 
It  was  not  to  be  expected  that  in  the  case  of 
this  axiom,  any  more  than  of  other  axioms,  there 
should  be  unanimity  among  thinkers  with  respect 
to  the  grounds  on  which  it  is  to  be  received  as 
true.  I  have  already  stated  that  I  regard  it  as 

*  But  though  it  is  a  condition  of  the  validity  of 
every  induction  that  there  be  uniformity  in  the  course 
of  nature,  it  is  not  a  necessary  condition  that  the  uni- 
formity should  pervade  all  nature.  It  is  enough  that 
it  pervades  the  particular  class  of  phenomena  to 
which  the  induction  relates.  An  induction  concern- 
ing the  motions  of  the  planets,  or  the  properties  of  the 
magnet,  would  not  be  vitiated  though  we  were  to  sup- 
pose that  wind  and  weather  are  the  sport  of  chance, 
provided  it  be  assumed  that  astronomical  and  mag- 
netic phenomena  are  under  the  dominion  of  general 
laws.  Otherwise  the  early  experience  of  mankind 
would  have  rested  on  a  very  weak  foundation  ;  for 
in  the  infancy  of  science  it  could  not  be  known  that 
all  phenomena  are  regular  in  their  course. 

Neither  would  it  be  correct  to  say  that  every  induc- 
tion by  which  we  infer  any  truth,  implies  the  general 
fact  of  imiformity  as  foreknown,  even  in  reference  to 
the  kind  of  phenomena  concerned.  It  implies,  either 
that  this  general  fact  is  already  known,  or  that  we 
may  now  know  it :  as  the  conclusion,  the  Duke  of 
Wellington  is  mortal,  drawn  from  the  instances  A,  B, 
and  C,  implies  either  that  we  have  already  concluded 
all  men  to  be  mortal,  or  that  we  are  now  entitled  to 
do  so  from  the  same  evidence.  A  vast  amount  of 
confusion  and  paralogism  respecting  the  grounds  of 
Induction  would  be  dispelled  by  keeping  in  view 
these  simple  considerations. 


362  QUOTATIONS   OK   INDUCTION. 

itself  a  generalization  from  experience.  Others 
hold  it  to  be  a  principle  which,  antecedently  to 
any  verification  by  experience,  we  are  compelled 
by  the  constitution  of  our  thinking  faculty  to  as- 
sume as  true.  Having  so  recently,  and  at  so 
much  length,  combated  a  similar  doctrine  as  ap- 
plied to  the  axioms  of  mathematics,  by  arguments 
which  are  in  a  great  measure  applicable  to  the 
present  case,  I  shall  defer  the  more  particular 
discussion  of  this  controverted  point  in  regard  to 
the  fundamental  axiom  of  induction,  until  a  more 
advanced  period  of  our  inquiry.  At  present  it 
is  of  more  importance  to  understand  thoroughly 
the  import  of  the  axiom  itself.  For  the  propo- 
sition, that  the  course  of  nature  is  uniform,  pos- 
sesses rather  the  brevity  suitable  to  popular,  than 
the  precision  requisite  in  philosophical  language  : 
its  terms  require  to  be  explained,  and  a  stricter 
than  their  ordinary  signification  given  to  them, 
before  the  truth  of  the  assertion  can  be  admitted. 
§  2.  Every  person's  consciousness  assures  him 
that  he  does  not  always  expect  uniformity  in  the 
course  of  events  ;  he  does  not  always  believe  that 
the  unknown  will  be  similar  to  the  known,  that 
the  future  will  resemble  the  past.  Nobody  be- 
lieves that  the  succession  of  rain  and  fine  weather 
will  be  the  same  in  every  future  year  as  in  the 
present.  Nobody  expects  to  have  the  same 
dreams  repeated  every  night.  On  the  contrary, 
every  body  mentions  it  as  something  extraordi- 
nary, if  the  course  of  nature  is  constant,  and  re- 
sembles itself,  in  these  particulars.  To  look  for 
constancy  where  constancy  is  not  to  be  expected, 


QUOTATIONS  ON  INDUCTION.  363 

as  for  instance  that  a  day  which  has  once  brought 
good  fortune  will  always  be  a  fortunate  day,  is 
justly  accounted  superstition. 

The  course  of  nature,  in  truth,  is  not  only  uni- 
form, it  is  also  infinitely  various.  Some  phenom- 
ena are  always  seen  to  recur  in  the  very  same 
combinations  in  which  we  met  with  them  at  first; 
others  seem  altogether  capricious  ;  while  some, 
which  we  have  been  accustomed  to  regard  as  bound 
down  exclusively  to  a  particular  set  of  combina- 
tions, we  unexpectedly  find  detached  from  some 
of  the  elements  with  which  we  had  hitherto  found 
them  conjoined,  and  united  to  others  of  quite  a 
contrary  description.  To  an  inhabitant  of  Central 
Africa,  fifty  years  ago,  no  fact  probably  appeared 
to  rest  on  more  uniform  experience  than  this, 
that  all  human  beings  are  black.  To  Europeans, 
not  many  years  ago,  the  proposition,  All  swans 
are  white,  appeared  an  equally  unequivocal  in- 
stance of  uniformity  in  the  course,  of  nature. 
Further  experience  has  proved  to  both  that  they 
were  mistaken  ;  but  they  had  to  wait  fifty  centu- 
ries for  this  experience.  During  that  long  time, 
mankind  believed  in  a  uniformity  of  the  course 
of  nature  where  no  such  uniformity  really  existed. 

According  to  the  notion  which  the  ancients  en- 
tertained of  induction,  the  foregoing  were  cases 
of  as  legitimate  inference  as  any  inductions  what- 
ever. In  these  two  instances,  in  which,  the  con- 
clusion being  false,  the  ground  of  inference  must 
have  been  insufficient,  there  was,  nevertheless,  as 
much  ground  for  it  as  this  conception  of  induction 
admitted  of.  The  induction  of  the  ancients  has 


364  QUOTATIONS   OK   INDUCTION. 

been  well  described  by  Bacon,  under  the  name 
of  u  Inductio  per  enumerationem  simplicem,  ubi 
non  reperitur  instantia  contradictoria. ' '  It  con- 
sists in  ascribing  the  character  of  general  truths  to 
all  propositions  which  are  true  in  every  instance 
that  we  happen  to  know  of.  This  is  the  kind  of 
induction  which  is  natural  to  the  mind  when  un- 
accustomed to  scientific  methods.  The  tendency, 
which  some  call  an  instinct,  and  which  others 
account  for  by  association,  to  infer  the  future 
from  the  past,  the  known  from  the  unknown,  is 
simply  a  habit  of  expecting  that  what  has  been 
found  true  once  or  several  times,  and  never  yet 
found  false,  will  be  found  true  again.  Whether 
the  instances  are  few  or  many,  conclusive  or  in- 
conclusive, does  not  much  affect  the  matter  : 
these  are  considerations  which  occur  only  on  re- 
flection ;  the  unprompted  tendency  of  the  mind 
is  to  generalize  its  experience,  provided  this  points 
all  in  one  direction  ;  provided  no  other  experience 
of  a  conflicting  character  comes  unsought.  The 
notion  of  seeking  it,  of  experimenting  for  it,  of 
interrogating  nature  (to  use  Bacon's  expression) 
is  of  much  later  growth.  The  observation  of  na- 
ture, by  uncultivated  intellects,  is  purely  passive  : 
they  accept  the  facts  which  present  themselves, 
without  taking  the  trouble  of  searching  for  more  : 
it  is  a  superior  mind  only  which  asks  itself  what 
facts  are  needed  to  enable  it  to  come  to  a  safe 
conclusion,  and  then  looks  out  for  these. 

But  though  we  have  always  a  propensity  to 
generalize  from  unvarying  experience,  we  are  not 
always  warranted  in  doing  so.  Before  we  can  be 


QUOTATIONS   ON   INDUCTION.  365 

at  liberty  to  conclude  that  something  is  univers- 
ally true  because  we  have  never  known  an  instance 
to  the  contrary,  we  must  have  reason  to  believe 
that  if  there  were  in  nature  any  instances  to  the 
contrary,  we  should  have  known  of  them.  This 
assurance,  in  the  great  majority  of  cases,  we  can 
not  have,  or  can  have  only  in  a  very  moderate 
degree.  The  possibility  of  having  it,  is  the 
foundation  on  which  we  shall  see  hereafter  that 
induction  by  simple  enumeration  may  in  some 
remarkable  cases  amount  practically  to  proof. 
No  such  assurance,  however,  can  be  had,  on  any 
of  the  ordinary  subjects  of  scientific  inquiry. 
Popular  notions  are  usually  founded  on  induction 
by  simple  enumeration  ;  in  science  it  carries  us 
but  a  little  way.  We  are  forced  to  begin  with 
it ;  we  must  often  rely  on  it  provisionally,  in  the 
absence  of  means  of  more  searching  investigation. 
But,  for  the  accurate  study  of  nature,  we  require 
a  surer  and  a  more  potent  instrument. 

It  was,  above  all,  by  pointing  out  the  insuf- 
ficiency of  this  rude  and  loose  conception  of  In- 
duction, that  Bacon  merited  the  title  so  generally 
awarded  to  him,  of  Founder  of  the  Inductive 
Philosophy.  The  value  of  his  own  contributions 
to  a  more  philosophical  theory  of  the  subject  has 
certainly  been  exaggerated.  Although  (along  with 
some  fundamental  errors)  his  writings  contain, 
more  or  less  fully  developed,  several  of  the  most 
important  principles  of  the  Inductive  Method, 
physical  investigation  has  now  far  outgrown  the 
Baconian  conception  of  Induction.  Moral  and 
political  inquiry,  indeed,  are  as  yet  far  behind 


366  QUOTATIONS   ON   INDUCTION. 

that  conception.  The  current  and  approved 
modes  of  reasoning  on  these  subjects  are  still  of 
the  same  vicious  description  against  which  Bacon 
protested  ;  the  method  almost  exclusively  em- 
ployed by  those  professing  to  treat  such  matters 
inductively,  is  the  very  inductioper  enumcrationem 
simplicem  which  he  condemns  ;  and  the  experi- 
ence which  we  hear  so  confidently  appealed  to  by 
all  sects,  parties,  and  interests,  is  still,  in  his  own 
emphatic  words,  mera  palpatio. 

§  3.  In  order  to  a  better  understanding  of  the 
problem  which  the  logician  must  solve  if  he 
would  establish  a  scientific  theory  of  Induction, 
let  us  compare  a  few  cases  of  incorrect  inductions 
with  others  which  are  acknowledged  to  be  legiti- 
mate. Some,  we  know,  which  were  believed  for 
centuries  to  be  correct,  were  nevertheless  incor- 
rect. That  all  swans  are  white,  can  not  have 
been  a  good  induction,  since  the  conclusion  has 
turned  out  erroneous.  The  experience,  however, 
on  which  the  conclusion  rested,  was  genuine. 
From  the  earliest  records,  the  testimony  of  the 
inhabitants  of  the  known  world  was  unanimous 
on  the  point.  The  uniform  experience,  therefore, 
of  the  inhabitants  of  the  known  world,  agreeing 
in  a  common  result,  without  one  known  instance 
of  deviation,  from  that  result,  is  not  always  suffi- 
cient to  establish  a  general  conclusion. 

But  let  us  now  turn  to  an  instance  apparently 
not  very  dissimilar  to  this.  Mankind  were  wrong, 
it  seems,  in  concluding  that  all  swans  were  white  : 
are  we  also  wrong,  when  we  conclude  that  all 
men's  heads  grow  above  their  shoulders,  and 


QUOTATIONS   ON   INDUCTION.  367 

never  below,  in  spite  of  the  conflicting  testimony 
of  the  naturalist  Pliny  ?  As  there  were  black 
swans,  though  civilized  people  had  existed  for 
three  thousand  years  on  the  earth  without  meet- 
ing with  them,  may  there  not  also  be  "  men 
whose  heads  do  grow  beneath  their  shoulders, ' ' 
notwithstanding  a  rather  less  perfect  unanimity 
of  negative  testimony  from  observers  ?  Most 
persons  would  answer  No  ;  it  was  more  credible 
that  a  bird  should  vary  in  its  color,  than  that  men 
should  vary  in  the  relative  position  of  their  prin- 
cipal organs.  And  there  is  no  doubt  that  in  so 
saying  they  would  be  right  :  but  to  say  why  they 
are  right,  would  be  impossible,  without  entering 
more  deeply  than  is  usually  done  into  the  true 
theory  of  Induction. 

Again,  there  are  cases  in  which  we  reckon  with 
the  most  unfailing  confidence  upon  uniformity, 
and  other  cases  in  which  we  do  not  count  upon  it 
at  all.  In  some  we  feel  complete  assurance  that 
the  future  will  resemble  the  past,  the  unknown 
be  precisely  similar  to  the  known.  In  others, 
however  invariable  may  be  the  result  obtained 
from  the  instances  which  have  been  observed,  we 
draw  from  them  no  more  than  a  very  feeble  pre- 
sumption that  the  like  result  will  hold  in  all  other 
cases.  That  a  straight  line  is  the  shortest  dis- 
tance between  two  points,  we  do  not  doubt  to  be 
true  even  in  the  region  of  the  fixed  stars.*  When 

*  In  strictness,  wherever  the  present  constitution 
of  space  exists  ;  which  we  have  ample  reason  to 
believe  that  it  does  in  the  reign  of  the  fixed  stars. 


368  QUOTATIONS   ON   INDUCTION. 

a  chemist  announces  the  existence  and  properties 
of  a  newly-discovered  substance,  if  we  confide  in 
his  accuracy,  we  feel  assured  that  the  conclusions 
he  has  arrived  at  will  hold  universally,  though  the 
induction  be  founded  but  on  a  single  instance. 
We  do  not  withhold  our  assent,  waiting  for  a 
repetition  of  the  experiment  ;  or  if  we  do,  it  is 
from  a  doubt  whether  the  one  experiment  was 
properly  made,  not  whether  if  properly  made  it 
would  be  conclusive.  Here,  then,  is  a  general  law 
of  nature,  inferred  without  hesitation  from  a 
single  instance  ;  a  universal  proposition  from  a 
singular  one.  Now  mark  another  case,  and  con- 
trast it  with  this.  Not  all  the  instances  which 
have  been  observed  since  the  beginning  of  the 
world,  in  support  of  the  general  proposition  that 
all  crows  are  black,  would  be  deemed  a  sufficient 
presumption  of  the  truth  of  the  proposition,  to 
outweigh  the  testimony  of  one  unexceptionable 
witness  who  should  affirm  that  in  some  region  of 
the  earth  not  fully  explored,  he  had  caught  and 
examined  a  crow,  and  had  found  it  to  be  gray. 

Why  is  a  single  instance,  in  some  cases,  suffi- 
cient for  a  complete  induction,  while  in  others, 
myriads  of  concurring  instances,  without  a  single 
exception  known  or  presumed,  go  such  a  very  little 
way  toward  establishing  a  universal  proposition  ? 
Whoever  can  answer  this  question  knows  more 
of  the  philosophy  of  logic  than  the  wisest  of  the 
ancients,  and  has  solved  the  problem  of  induction. 

(pp.  431—432).  What  renders  arithmetic  the 
type  of  a  deductive  science,  is  the  fortunate  ap- 
plicability to  it  of  a  law  so  comprehensive  as 


QUOTATIONS   OX   INDUCTION.  369 

i  i  The  sums  of  equals  are  equals' ' :  or  (to  express 
the  same  principle  in  less  familiar  but  more  char- 
acteristic language),  whatever  is  made  up  of 
parts,  is  made  up  of  the  parts  of  those  parts. 
This  truth,  obvious  to  the  senses  in  all  cases  which 
can  be  fairly  referred  to  their  decision,  and  so 
general  as  to  be  co- extensive  with  nature  itself, 
being  true  of  all  sorts  of  phenomena  (for  all  ad- 
mit of  being  numbered),  must  be  considered  an 
inductive  truth,  or  law  of  nature,  of  the  highest 
order.  And  every  arithmetical  operation  is  an 
application  of  this  law,  or  of  other  laws  capable 
of  being  deduced  from  it.  This  is  our  warrant 
for  all  calculations.  We  believe  that  five  and  two 
are  equal  to  seven,  on  the  evidence  of  this  in- 
ductive law,  combined  with  the  definitions  of 
those  numbers.  We  arrive  at  that  conclusion  (as 
all  know  who  remember  how  they  first  learned  it) 
by  adding  a  single  unit  at  a  time  :  5+1  =  6, 
therefore  5+1  +  1  =  6+1  =  7  ;  and  again  2  =  1 
+1,  therefore 


QUOTATIONS  ON  INTERPRETATION. 


APPENDIX  J. 

234.  1.  From  Davies  and  Peck,  Dictionary 
of  Mathematics. 

Interpretation.  [L.  interpretatio,  explana- 
tion]. The  process  of  explaining  results  arrived 
at  by  the  application  of  mathematical  rules. 
When,  for  example,  an  algebraic  definition  is 
laid  down,  there  is  frequently  some  restriction 
implied  in  making  the  definition,  so  that  the  re- 
sult to  which  it  leads  presents  more  cases  than  can 
be  explained  by  it,  or  even  than  was  contemplated 
by  it.  Thus  the  abbreviation  of  a  a,  a  a  a,  into 
a2,  a3,  and  the  rules  which  spring  from  it,  lead 
to  results  of  the  form. 

a  ~2,  a°,  a*,  a  ~  *,  etc. 

These  results,  until  interpreted,  are  without  any 
intelligent  algebraic  meaning. 

When  such  results  arise,  the  province  of  inter- 
pretation begins  ;  their  meaning  and  force  are 
investigated  and  explained,  and  the  definitions 
heretofore  too  narrow,  are  extended  so  as  to  cover 
these  and  other  results. 

The  rule  to  be  adopted  in  interpreting  new  ex- 
pressions obtained  by  applying  known  processes, 
is  to  attribute  to  them  such  a  meaning  as  to  make 


QUOTATIONS  ON   INTERPRETATION.     371 

the  whole  of  the  process  true  by  which  they  were 
obtained.  For  example  :  the  formula 

am  X  «n  =  am  +  n 

is  perfectly  intelligible  so  long  as  m  and  n  are 
whole  numbers.  Suppose  it  were  required  to  in- 
terpret the  symbol  a°,  that  is,  to  give  to  it  such 
a  meaning,  that  the  above  formula  shall  be  true 
in  that  case.  Making  m=0,  the  formula  becomes 

a°  X  an  —  «°  +  n  =  «n  ', 

hence,  a°  =  1.  Again,  suppose  it  were  required 
to  interpret  the  symbol  a*.  Make  m  =  ^  and 
91  =  ,  and  the  formula  becomes 


hence,  a*6  =  V«,  for  ^a  x  ^«  =  «,  by  definition. 

Besides  the  application  of  the  principles  of  in- 
terpretation to  the  explanation  of  new  symbols, 
another  very  important  application  consists  in 
making  suppositions  upon  certain  arbitrary  quan- 
tities which  enter  formulas,  and  then  comparing 
the  results  with  known  facts,  thus  deducing  new 
truths.  As  an  example  of  this  method  of  inter- 
pretation let  us  take  the  equation  of  the  ellipse 


and   suppose   x  >  a,  finding  the  value  of  y  in 
terms  of  a;,  we  have 


372     QUOTATIONS   ON   INTERPRETATION. 

from  which  we  see  that  for  all  values  of  x  greater 
than  a,  y  is  imaginary.  Now  an  imaginary 
result  indicates  an  impossibility  in  the  assumption. 
Hence,  we  interpret  the  result  as  indicating  that 
no  point  of  the  ellipse  can  lie  at  a  greater  distance 
from  its  conjugate  axis  than  the  extremity  of  the 
transverse  axis. 

In  integrating  the  differential  of  a  transcen- 
dental function  by  an  algebraic  rule,  a  result  oo  is 
reached,  which  is  manifestly  absurd,  since  no 
function  can  be  oo.  We  interpret  this  as  indi- 
cating that  the  rule  fails  in  the  case  considered. 

2.   From  Smith's  Synonyms  Discriminated. 

Expound  (Lat.  expono)  denotes  sustained  ex- 
planation ;  while  a  mere  word  or  phrase  may 
be  explained,  a  whole  work  or  parts  of  it  may 
be  expounded.  Exposition  is  continuous  crit- 
ical explanation.  Interpret  (Lat.  interpres, 
an  interpreter),  beyond  the  mere  sense  of  verbal 
translation  from  one  language  to  another,  conveys 
the  idea  of  private  or  personal  explanation  of 
what  is  capable  of  more  than  one  view.  Hence 
interpretation  is  more  arbitrary  than  exposition, 
and  more  theoretical  than  explanation.  Expound 
relates  only  to  words  in  series,  interpretation  is 
applicable  also  to  anything  of  a  symbolical  char- 
acter, as  to  interpret  a  dream  or  a  prophecy.  It 
is  also,  in  common  with  explain,  an  application 
to  anything  which  may  be  viewed  in  different 
lights,  as  the  actions  of  men.  In  this  way,  to 
explain  conduct  would  rather  be  to  account  for 
it  ;  to  interpret  it  would  be  to  assign  motives  or 
significance  to  it.  Explanation  deals  with  facts, 
interpretation  with  causes  also. 


QUOTATIONS  ON  DEDUCTION. 


APPENDIX  K. 


235.  1.  From  Fleming's  Vocabulary  of  Phi- 
losophy,  Ed.  1858,  pp.  126-7. 

Deduction  (from  deduce,  to  draw  from,  to 
cause  to  come  out  of,)  is  the  mental  operation 
which  consists  in  drawing  a  particular  truth  from 
a  general  principle  antecedently  known.  It  is 
opposed  to  induction,  which  consists  in  rising 
from  particular  truths  to  the  determination  of 
a  general  principle.  Let  it  be  proposed  to  prove 
that  Peter  is  mortal  ;  I  know  that  Peter  is  a 
man,  and  this  enables  me  to  say  that  all  men  are 
mortal,  from  which  affirmation  I  deduce  that 
Peter  is  mortal. 

The  syllogism  is  the  form  of  deduction.  Aris- 
totle (Prior.  Analyt.,\\b.  1,  cap.  1)  has  defined 
it  to  be  "  an  enunciation  in  which  certain  asser- 
tions being  made,  by  their  being  true,  it  follows 
necessarily,  that  another  assertion  different  from 
the  first  is  true  also. ' ' 

Before  we  can  deduce  a  particular  truth,  we 
must  be  in  possession  of  the  general  truth.  This 
may  be  acquired  intuitively,  as  every  change 
implies  a  cause  ;  or  inductively,  as  the  volume 
of  gas  is  in  the  inverse  ratio  of  the  pressure. 

Deduction,  when  it  uses  the  former  kind  of 


374  QUOTATIONS   ON   DEDUCTION. 

truths,  is  demonstration  or  science.  Truths 
drawn  from  the  latter  kind  are  contingent  and . 
relative,  and  admit  of  correction  by  increasing 
knowledge.  The  principle  of  deduction  is,  that 
things  that  agree  with  the  same  things  agree  with 
one  another.  The  principle  of  induction  is,  that 
in  the  same  circumstances,  and  in  the  same  sub- 
stances, from  the  same  causes  the  same  effects 
will  follow. 

The  mathematical  and  metaphysical  sciences 
are  founded  on  deduction,  the  physical  sciences 
rest  on  induction, 

2.  From  Day's  Elements  of  Logic,  Ed.  1868, 
p.  105. 

A  Deductive  Syllogism  is  a  Mediate  Reasoning 
in  which  the  movement  of  Thought  is  from  a 
Whole  to  a  Part,  mediated  through  a  middle 
term,  which  is,  respectively,  a  part  of  that  whob 
and  a  whole  of  that  part ;  as,  Man  is  mortal ;  Caius 
is  a  man  ;  therefore,  Caius  is  mortal. 

As  the  Deductive  Syllogism  is  a  Mediate 
Reasoning,  its  datum  must  consist  of  two  Judg- 
ments, which,  as  given  to  Thought,  are  not  of 
course  at  all  validated  by  the  Reasoning. 

They  must  be  regarded  consequently  as  only 
assumed  for  the  Reasoning,  or  must  rest  on  evi- 
dence foreign  to  it.  But  the  movement  of 
Thought  in  itself  may  be  valid,  although  the  given 
Judgments  are  false  ;  just  as  an  arithmetical  pro- 
cess may  be  correct,  although  applied  to  unreal 
objects. 

3.  From   Bowen's  Logic,  Ed.  1874,  pp.  261, 
262. 


QUOTATIONS   ON   DEDUCTION.  375 

Reasoning,  however,  proceeds  not  only  in  dif- 
ferent wholes,  but  in  different  aspects  of  the  same 
whole.  We  may,  it  is  evident,  regard  any  whole, 
considered  as  the  complement  of  its  parts,  in 
either  of  two  ways  ;  for  we  may,  on  the  one  hand, 
look  from  the  whole  to  the  parts,  and  reason  ac- 
cordingly downwards  ;  or,  on  the  other  hand,  look 
from  the  parts  to  the  whole  they  constitute,  and 
reason  accordingly  upwards.  The  former  of  these 
reasonings  is  called  Deductive,  the  latter  Induc- 
tive. Deductive  reasoning  is  founded  on  the 
maxim,  '  What  belongs  to  the  containing  whole 
belongs  also  to  the  contained  parts  ;'  Induction, 
on  the  contrary  maxim,  i  What  belongs  to  the 
constituent  parts  belongs  also  to  the  constituted 
whole.'  Thus,  in  Deductive  reasoning,  the 
whole  is  stated  first,  and  what  is  affirmed  of  it  is 
affirmed  of  the  parts  it  contains  ;  in  other  words, 
a  general  law  is  laid  down,  and  predicated  of  the 
particular  instances  to  which  it  applies. 

In  Inductive  reasoning,  the  parts  are  first  stated, 
and  what  is  predicated  of  them  is  also  predicated 
of  the  whole  they  constitute  ;  in  other  words,  the 
particular  instances  are  first  'stated  as  facts,  and 
then  the  law  they  constitute  is  evolved. 

4.  From  Hedge's  Elements  of  Logick,  Ed. 
1854,  pp.  118,  119. 

Syllogism  (= Deduction)  and  induction  pro- 
ceed in  opposite  directions.  Induction  .  .  begins 
with  individual  objects,  as  they  exist  in  nature, 
and  ascends  by  successive  steps  to  the  most 
general  truths.  Syllogism  (=: Deduction)  begins 
where  inductions  terminates.  It  commences  with 


376  QUOTATIONS   ON   DEDUCTION. 

some  universal  proposition,  and  follows  back  the 
footsteps  of  the  former  process,  transferring  at 
each  stage  the  predicate  of  the  more  general  to 
the  less  general  rank  of  beings  ;  or,  in  other 
words,  predicating  the  genus  of  the  species,  and 
the  species  of  the  individual. 

.  .  .  Syllogism  (= Deduction)  is  employed 
with  advantage  in  communicating  to  others,  in 
an  exact  and  perspicuous  manner,  the  general 
principles  of  science.  It  may  also  be  used  with 
success  in  exposing  the  weakness  of  arguments, 
stated  in  loose  or  figurative  language.  But  it 
is  of  no  service  in  helping  us  to  the  discovery 
of  new  truths.  ' '  We  must  know  a  thing  first, ' ' 
Mr.  Locke  observes,  "  and  then  we  can  prove  it 
syllogisticallj-  " 


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Constitution  of  the  State  of  New  York  as  amended  at  the  election  of  1882, 
the  Constitution  of  the  United  States,  and  the  Declaration  of  Independence, 
etc.,  etc.    By  HENRY  C.  NORTHAM.    16mo,  cloth,  pp.  185.    75  cts. 

Is  it  that  this  book  was  made  because  the  times  demanded  it,  or  that  the 
publication  of  a  book  which  made  the  teaching  of  Civil  Government  practi- 
cable led  to  a  general  desire  that  it  should  be  taught  ?  Certain  it  is  that  this 
subject,  formerly  regarded  as  a  "  finishing  "  branch  in  the  high  school,  is 
now  found  on  every  teacher's  examination-paper,  and  is  commonly  taught 
in  district  schools.  Equally  certain  is  it  that  in  the  State  of  New  York  this 
text-book  is  used  more  than  all  others  combined. 

2.  A  Chart  of  Civil  Government.    By  CHARLES  T.  POOLER.    Sheets  12xl8r 
5  cts.    The  same  folded,  in  cloth  covers,  25  cts. 

Schools  using  Northam's  Civil  Government  will  find  this  chart  of  great 
use,  and  those  not  yet  ready  to  introduce  a  text-book  will  be  able  to  give  no 
little  valuable  instruction  by  the  charts  alone.  Some  commissioners  have 
purchased  them  by  the  hundred  and  presented  one  to  every  school  house  in 
the  county. 

8.  Handbook  for  School  Teachers  and  Trustees.  A  manual  of  School 
Law  for  School  Officers,  Teachers  and  Parents  in  the  State  of  New  York. 
By  HERBERT  BROWNELL.  16mo,  leatherette,  pp.  64.  35  cts. 

This  is  a  specification  of  the  general  subject,  presenting  clearly,  defi- 
nitely, and  with  references,  important  questions  of  School  Law.  Particular 
attention  is  called  to  the  chapters  treating  of  schools  under  visitation  of  the 
Regents— a  topic  upon  which  definite  information  is  often  sought  for  in  vain. 

h.  t  Common  School  Law  for  Common  School  Teachers.  A  digest  of  the 
provisions  of  statute  and  common  law  as  to  the  relations  of  the  Teacher  to 
the  Pupil,  the  Parent,  and  the  District.  With  500  references  to  legal  decis- 
ions in  28  different  States.  14th  edition,  wholly  re-written,  with  references 
to  the  new  Code  of  1888.  By  C.  W.  BARDEEN.  16mo,  cloth,  pp.  120.  75  cts. 

This  has  been  since  1875  the  standard  authority  upon  the  teacher's  rela- 
tions, and  is  frequently  quoted  in  legal  decisions.  The  new  edition  is  much 
more  complete  than  its  predecessors,  containing  Topical  Table  of  Contents, 
and  a  minute  Index. 

5.  Laics  of  New  York  relating  to  Common  Schools,  with  comments  and 
instructions,  and  a  digest  of  decisions.    8vo,  leather,  pp.  867.    $4.00. 

This  is  what  is  known  as  u  The  New  Code  of  1888,"  and  contains  all  re- 
visions of  the  State  school-law  to  date. 

6.  The  Powers  and  Duties  of  Officers  and  Teachers.    By  ALBERT  P.  MAR- 
BLE.   16mo,  paper,  pp.  27.    15  cts. 

A  vigorous  presentation  in  Sup't  Marble's  pungent  style  of  tendencies 
as  well  as  facts. 

7.  First  Principles  of  Political  Economy.    By  JOSEPH  ALDEN.    16mo, 
cloth,  pp.  153.    75  cts. 

Ex-President  Andrew  D.  White  says  of  this  book  :  "  It  is  clear,  well 
arranged,  and  the  best  treatise  for  the  purpose  I  have  ever  seen." 

C.  W.  BARDEEN,  Publisher,  Syracuse,  N.  Y. 


•* THE  SCHO  OL  B  ULLETIN  PUBLZCA  TIONS. 

Teachers'  Question  Books. 

1.  The  Regents'  Questions  in  Arithmetic,  Geography,  Grammar  and  Spell- 
ing from  the  first  examination  in  1866  to  June  1882.  (No  questions  of  later  date 
will  be  printed.}  Being  the  11,000  Questions  for  the  preliminary  examinations 
for  admission  to  the  University  of  the  State  of  New  York,  prepared  by  the 
Regents  of  the  University,  and  participated  in  simultaneously  by  more  than 
250  academies,  forming  a  basis  for  the  distribution  of  more  than  a  million  of 
•dollars.  Complete  with  Key.  Cloth,  16mo,  pp.  473.  $2.00. 

9.    Complete.    The  same  as  above  but  without  answers.    Pp.  340.    $1.00. 

In  the  subjects  named,  no  other  Question  Book  can  compare  with  this 
•either  in  completeness,  in  excellence,  or  in  popularity.  By  Legislative  Enact- 
ment no  lawyer  can  be  admitted  to  the  bar  in  the  State  of  New  York  without 
passing  a  Regents'  Examination  in  these  subjects. 

3.  The  Dime  Question  Books,  with  full  answers,  notes,  queries,  etc.  Paper, 
pp.  about  40.  By  A.  P.  SOTJTHWICK.  Each  10  cts. 

Elementary  Series.  Advanced  Series. 

3.  Physiology.  1.  Physics. 

4.  Theory  and  Practice.  2.  General  Literature, 
6.  U.  S.  History  and  Civil  Gov't.  5.  General  History. 

10.  Algebra.  7.  Astronomy. 

13.  American  Literature.  8.  Mythology. 

14.  Grammar.  9.  Rhetoric. 

15.  Orthography  and  Etymology.  11.  Botany. 

18.  Arithmetic.  12.  ZoOlogy. 

19.  Physical  and  Political  Geog.  16.  Chemistry. 
50.  Reading  and  Punctuation.  17.  Geology. 

These  10  in  one  book.    Cloth,  $1.00.         These  10  in  one  book.    Cloth,  $1.06. 
Extra  Volume,  21.  Temperance  Physiology. 

The  immense  sale  of  the  Regents'  Questions  in  Arithmetic,  Geography, 
Grammar,  and  Spelling  has  led  to  frequent  inquiry  for  the  questions  in  the 
Advanced  Examinations.  -4s  it  is  not  permitted  to  reprint  these,  we  have  had 
prepared  this  series,  by  which  the  teacher  need  purchase  books  only  on  the 
subjects  upon  which  special  help  is  needed.  Frequently  a  $1.50  book  is 
bought  for  the  sake  of  a  few  questions  in  a  single  study.  Here,  the  studies 
may  be  taken  up  one  at  a  time,  a  special  advantage  in  New  York,  sinct  appli- 
•cants for  State  Certificates  may  nmv  present  themselves  for  examination  in  only 
part  of  the  subjects,  'and  receive  partial  Certificates  to  be  exchanged  for  full  Cer- 
tificates when  all  the  branches  have  been  passed.  The  same  plan  is  very  gener- 
ally pursued  by  county  superintendents  and  commissioners  who  are  encour- 
ing  their  teachers  to  prepare  themselves  for  higher  certificates. 

U.  Quizzism.  Quirks  and  Quibbles  from  Queer  Quarters.  Being  a  Melange 
of  questions  in  Literature,  Science,  History,  Biography,  Mythology,  Philolo- 
gy, Geography,  etc.  By  A.  P.  SOUTHWICK.  16mo,  pp.  55.  25  cts.  Key,  $1.00. 

A  stimulus  for  home  study,  and  invaluable  for  school  or  teachers' 
gatherings. 

5.  New  York  State  Examination  Questions.    Cloth,  16mo,  pp.  256.    50  cts. 
This  contains  all  the  questions  given  at  all  the  New  York  Examinations 

for  State  Certificates  from  the  beginning.    There  are  more  questions  and  in 
greater  variety  than  in  any  other  collection.    It  does  not  give  answers. 

6.  The  Common  School  Question  Book.    By  ASA  L.  CRAIG.    Cloth,  12 mo, 
pp.  340.    $1.50.    We  can  also  furnish  SHAW'S  National  Question  Book,  pp.  351, 
$1.50 ;  STILLWELL'S  Practical  Question  Book,  pp.  400,  $1.50  ;  BROWN'S  Common 
School  Examiner,  pp.  371,  $1.00:   THOMPSON'S  Teachers  Examiner^  pp.  378 
$1.50;    SHERRILL'S  Normal  Question  Book,  pp.  460,  $1.50. 

C.  W.  BARDEE^,  Publisher,  Syracuse,  N,  Y. 


-THE  SCHOOL  BULLETIN  PUBLICATIONS.- 


Helps  toward  Correct  Speech. 

1.  Verbal  Pitfalls:  a  manual  of  1500  words  commonly  misused,  includ- 
ing all  those  the  use  of  which  in  any  sense  has  been  questioned  by  Dean. 
Alvord,  G.  W.  Moon,  Fitzedward  Hall,  Archbishop  Trench,  Wm.  C.  Hodg- 
son, W.  L.  Blackley,  G.  F.  Graham,  Richard  Grant  White,  M.  Schele  de  Vere, 
Wm.  Mathews,  "  Alfred  Ayres,"  and  many  others.  Arranged  alphabetically » 
with  3000  references  and  quotations,  and  the  ruling  of  the  dictionaries. 
By  C.  W.  BARDEEN.  16ino,  cloth,  pp.  223.  75  cts. 

Perhaps  the  happiest  feature  of  the  book  is  its  interesting  form.  Some 
hundreds  of  anecdotes  have  been  gathered  to  illustrate  the  various  points 
made.  These  have  the  advantage  not  only  of  making  the  work  entertain- 
ing, but  of  fixing  the  point  in  the  mind  as  a  mere  precept  could  not  do.  The 
type  indicates  at  a  glance  whether  the  use  of  a  word  is  (1)  indefensible,  (2} 
defensible  but  objectionable,  or  (3)  thoroughly  authorized. 

*.  A  System  of  Rlietoric.  By  C.  W.  BARDEEN.  12mo,  half  leather,  pp. 
813.  $1.75. 

3.  A  SJwrter  Course  in  Rhetoric.  By  C.  W.  BABDEEN.  12mo,  half  leather, 
pp.  311.  $1.00. 

It.  Outlines  of  Sentence  Making.  By  C.  W.  BARDEEN.  12mo,  cloth,  pp. 
187.  75  cts. 

5.  Practical  PJionics.    A  comprehensive  study  of  Pronunciation,  form- 
ing a  complete  guide  to  the  study  of  elementary  sounds  of  the  English  Lan- 
guage, and  containing  3,000  words  of  difficult  pronunciation,  with  diacriti- 
cal marks  according  to  Webster's  Dictionary.    By  E.  V.  DE  GRAFF.    16mo, 
cloth,  pp.  108.    75  cts. 

The  "book  before  us  is  the  latest,  and  in  many  respects  the  best,  of  the 
manuals  prepared  for  this  purpose.  The  directions  for  teaching  elementary 
sounds  are  remarkably  explicit  and  simple,  and  the  diacritical  marks  a  r& 
fuller  than  in  any  other  book  we  know  of,  the  obscure  vowels  being  mai  kod, 
as  well  as  the  accented  ones.  This  manual  is  not  like  others  of  the  kind,  a 
simple  reference  book.  It  is  meant  for  careful  study  and  drill,  and  is  es- 
pecially adapted  to  class  use.— New  England  Journal  of  Education. 

6.  Pocket  Pronunciation  Book,  containing  the  3,000  words  of  difficult 
pronunciation,  with  diacritical  marks  according  to  Webster's  Dictionary. 
By  E.  V.  DE  GRAFF.    16mo,  manilla,  pp.  47.    15  cts. 

Every  vowel  that  can  possibly  be  mispronounced  is  guarded  by  danger 
signals  which  send  one  back  to  the  phonic  chart  for  instructions.  We  are 
glad  to  notice  that  the  Professor  is  leading  a  campaign  against  the  despoil 
ers  of  the  vowel  u  ;  he  cannot  hold  communion  with  an  educated  man  whose 
third  day  in  the  week  is  "Toosday."— Northern  Christian  Advocate. 

7.  Studies  in  Articulation :  a  study  and  drill-book  in  the  Alphabetic  Ele- 
ments of  the  English  language.    Fifth  thousand.    By  J.  H.  HOOSE.    16mo, 
cloth,  pp.  70.    50  cts. 

This  work  not  only  analyzes  each  sound  in  the  language,  but  gives  as 
illustrations  hundreds  of  words  commonly  mispronounced. 

Dr.  Hoose's  "  Studies  in  Articulation  "  is  the  most  useful  manual  of  the 
kind  that  I  know  of.  It  should  be  a  text-book  in  every  Teachers'  Institute. 
—A.  J.  Rickoff,  formerly  Sujft  of  Schools  at  Cleveland  and  at  Yonkers. 

8.  Hints  on  Teaching  Orthoepy.    By  CHAS.  T.  POOLER.    16mo,  paper,  pp. 
15.    10  cts. 

9.  Question  Book  of  Orthography,  Orthoepy,  and  Etymology^  with  Notes, 
Queries,  etc.    By  ALBERT  P.  SOUTHWICK.    16mo,  paper,  pp.  40,    10  Jts. 

10.  Question  Book  of  Reading  and  Punctuation,  with  Notes,  Queries,  etc. 
By  ALBERT  P.  SOUTHWICK.  16mo,  paper,  pp.  38.  10  cts. 

C.  W.  BARDEEtf,  Publisher,  Syracuse,  N.  Y. 


THE  SCHOOL  BULLETIN  PUBLICATIONS. 

Helps  in  Language  Teaching. 

1.  Normal  Language  Lessons :  being  the  instruction  in  Grammar  given 
at  the  Cortland  State  Normal  School.    By  Prof.  S.  J.  SORNBERGER.    16mo, 
boards,  pp.  81.    50  cts. 

Whatever  text-book  the  teacher  uses,  or  if  he  uses  no  text-book  at  all, 
he  will  find  this  manual  of  great  assistance.  Its  classification  is  simple,  its 
definitions  are  careful,  its  tabular  analyses  are  complete,  and  Us  reference  by 
page  to  ail  the  best  autJiors  makes  it  invaluable. 

2.  Exercises  in  English  Syntax.    By  A.  G.  BUGBEE.    16mo,  leatherette, 
pp.  87.    35  cts. 

This  differs  from  other  handbooks  of  sentences  for  class-drill  in  that  it 
does  not  print  wrong  sentences  to  be  corrected,— a  practice  now  generally 
condemned,  because  incorrect  forms  should  never  be  put  before  the  child's 
eye:— but  leaves  blanks  in  the  sentence  to  be  filled  by  the  pupil  from  a 
choice  of  expressions  given,  thus  calling  in  the  most  effective  way  to  right 
usage  and  its  reasons.  It  is  of  especial  assistance  in  preparation  for  Re- 
gents' examinations,  which  always  include  much  work  of  this  kind.  Send 
for  special  circular  with  specimen  sentences,  and  recommendations. 

8.  The  Regents'  Questions  in  Grammar,  from  the  beginning  to  June, 
1882.  By  DANIEL  J.  PRATT,  Assistant  Secretary.  16mo,  manilla,  pp.  109. 
25  cts. 

This  unequalled  series  of  questions  is  recognized  throughout  the  country 
as  the  best  drill-book  ever  made,  and  the  only  satisfactory  preparation  for 
examination. 

An  edition  of  these  Questions,  with  complete  answers,  and  references  to  the 
grammars  of  Brown,  Murray,  Greene,  Clark,  Kerl,  Quackenbos,  Weld  & 
Quackenbos,  Hart-,  Fowler,  Swinton,  Reed  &  Kellogg,  and  Whitney,  will  be 
sent  post-paid  to  any  address  on  receipt  of  One  Dollar.  It  contains  198 
pages,  and  is  handsomely  bound  in  cloth. 

U.  Dime  Question  Book  No.  lit,  Grammar.  By  ALBERT  P.  SOUTHWICK. 
KJmo,  paper,  pp.  35.  10  cts. 

This  is  one  of  the  best  books  in  a  deservedly  popular  series,  giving  full 
answers  to  every  question,  with  notes,  queries,  etc.  Conductor  John  Ken- 
nedy says:  "  The  bad  question  book  fosters  cram;  the  good  one  suggests 
study.  Mr.  Southwick's  system  is  good.  It  is  happy  and  nourishing.  I 
hope  you  may  sell  a  million  of  them." 

5.  The  Diacritical  Speller.    A  practical  course  of  exercises  in  Spelling 
and  Pronunciation.    By  C.  R.  BALES.    8vo,  boards,  pp.  68.    50  cts. 

This  work  is  novel  even  in  a  field  so  thoroughly  worked  as  spelling.  Its 
striking  features  are  conciseness  and  simplicity.  The  pupil  is  not  drilled 
upon  what  all  pupils  know,  but  only  upon  what  most  pupils  fail  in.  The 
collections  of  words  are  made  with  great  skill,  and  the  pupil  who  uses  this 
book  is  not  likely  to  say  Toosday  or  Reuler.  The  selection  of  test-words  is 
particularly  happy,  and  the  exercises  in  synonyms  will  afford  material  for 
many  a  spare  ten  minutes.—  California  Teacher. 

6.  An  Aid  to  English   Grammar;  designed  principally  for  Teachers. 
By  ASHER  P.  STARKWEATHER.    IGmo,  boards,  pp.  230.    75  cts. 

This  is  a  grammar  aid  book  on  a  wholly  original  plan.  It  is  simply  a 
collection  of  words  which  are  used  as  two  or  more  parts  of  speech,  with 
illustrative  sentences  to  show  their  correct  use. — School  Herald,  Chicago. 

C,  W.  BAItDEEN,  Publisher,  Syracuse,  N.  Y. 


-THE  SCiIOOL  BULLETIN  PUBLICATIONS.- 


Helps  in  Teaching  Literature. 

1.  A  Series  of  Questions  in  English  and  American  Literature,  prepared 
for  class  drill  and  private  study  by  MARY  F.  HENDRICK,  teacher  in  the  State 
Normal  School,  Cortland,  N.  Y.    16mo,  boards,  pages  100,  interleaved.   35  cts. 

This  edition  is  especially  prepared  for  taking  notes  in  the  literature 
class,  and  may  be  used  in  connection  with  any  text-book  or  under  any  in- 
struction. 

2.  Early  English  Literature,  from  the  Lay  of  Beowulf  to  Edmund  Spen- 
ser.   By  WM.  B.  HARLOW,  instructor  in  the  High  School,  Syracuse,  N.  Y. 
16mo,  cloth,  pp.  138.    75  cts. 

This  handsome  volume  gives  copious  extracts  from  all  leading  authors, 
of  sufficient  length  to  afford  a  fair  taste  of  their  style,  while  its  biographical 
and  critical  notes  give  it  rare  value. 

3.  Dime  Question  Book  No.  2,  General  Literature,  and  No.  13,  American, 
Literature.    By  ALBERT  P;  SOUTHWICK.    16mo,  paper,  pp.  35,  39.    10  cts.  each. 

These  are  among  the  most  interesting  books  in  the  series,  abounding  in 
allusion  and  suggestion,  as  well  as  giving  full  answers  to  every  question. 
They  afford  a  capital  drill,  and  should  be  used  in  every  class  as  a  prepara- 
tion for  examination. 

h.  How  to  Obtain  the  Greatest  Value  from  a  Book.  By  the  Rev.  R.  W. 
LOWRIE.  8vo,  pp.  12.  25  cts. 

No  one  can  read  this  essay  without  pleasure  and  profit. 

5.  The  Art  of  Questioning.    By  JOSHUA  G.  FITCH.    16mo,  paper,  pp.  36. 
15  cts. 

Mr.  Fitch,  one  of  Her  Majesty's  inspectors  of  schools,  now  recognized  as 
the  ablest  of  English  writers  on  education,  owed  his  early  reputation  to  this 
address,  the  practical  helpfulness  of  which  is  everywhere  acknowledged. 

6.  The  Art  of  Securing  Attention.    By  JOSHUA  G.  FITCH.    16mo,  paper, 
pp.  43.    15  cts. 

The  Maryland  School  Journal  well  says:  "  It  is  itself  an  exemplification 
of  the  problem  discussed,  for  the  first  page  fixes  the  attention  so  that  the 
reader  never  wearies,  till  he  comes  to  the  last  and  then  wishes  that  the  end 
had  not  come  so  soon." 

7.  The  Elocutionist's  Annual,  comprising  new  and  popular  Readings, 
Recitations,  Declamations,  Dialogues,  Tableaux,  etc.,  etc.     Compiled  oy 
Mrs.  J.  W.  SHOEMAKER.    Paper,  16mo,  pp.  200.    12  Numbers.    Price  of  each, 
30  cts. 

Though  primarily  designed  for  classes  in  elocution,  the  character  of  the 
selections  is  so  high  that  any  of  these  volumes  may  be  used  with  profit  in  a 
literature  class. 

S.  The  Bible  in  the  Public  Schools.  Paper,  24mo,  2  vols.,  pp.  214,  £28. 
50  cts. 

These  volumes  contain  the  most  important  arguments,  decisions,  and 
addresses  connected  with  the  celebrated  contest  in  Cincinnati,  1869. 

C.  W.  BARDEEN,  Publisher,  Syracuse,  N.  Y, 


-THE  SCHOOL  BULLETIN  PUBLICATIONS.- 


Helps  in  t  Teaching  History. 

1.  A  Thousand  Questions  in  Ame?*ican  History.    16mo,  cloth,  pp.  347. 
Price  $1.00. 

This  work  has  been  prepared  by  an  eminent  teacher  for  use  in  his  own 
school— one  of  the  largest  in  the  State.  It  shows  rare  breadth  of  view  and 
•discrimination,  dealing  not  merely  with  events  but  with  causes,  and  with  th« 
side-issues  that  have  so  much  to  do  with  determining  the  destiny  of  a  nation. 

2 .  Helps  in  Fixing  tlie  Facts  of  Amei^ican  History.    By  HENRY  C.  NOR- 
THAM.    16mo,  cloth,  pp.  298.    Price  $1.00.  <  ^ 

Here  all  facts  are  presented  in  groups.    The     .  L— exington.  _ 
key-word  to  the  Revolution,  for  instance,  is       I— independence.  >^ 
LIBERTY,  as  shown  in  the  accompanying  table       B— urgoyne's  Surrender.1 
•of  Key-Words  •  and  in  like  manner  the  events  of       E— vacuation. 
the  late  civil  war  are  kept  chronologically  dis-       R— etribution. 
tinct  by  the  key-words  SLAVES  FREED.   Chart       T— reason,  f 
^"o.  1  indicates  by  stars  the  years  in  each  decade       Y— orktown.  v 
from  1492  to  1789,  in  which  the  most  remarkable  events  occured,  while  tht 
•colored  chart  No.  2  arranges  the  events  in  twelve  groups. 

5.  Topics  and  References  in  American  History,  with  numerous»Searoh 
Questions.  By  GEO.  A.  WILLIAMS.  IGmo,  leatherette,  pp.  50.  50  cts. 

This  is  a  book  of  immediate  practical  value  to  every  teacher.  The  refer- 
ences are  largely  to  the  lighter  and  more  interesting  illustrations  of  history, 
of  a  kind  to  arouse  the- thought  of  pupils  by  giving  vivid  conceptions  of  th« 
events  narrated.  By  dividing  these  references  among  the  members  of  a  class, 
the  history  recitation  may  be  made  the  most  delightful  of  the  day. 

U.  Dime  Question  Books,  No.  5,  General  History,  and  No.  6,  United  States 
History  and  Civil  Government.  By  ALBERT  P.  SOUTHWICK.  16mo,  paper,  pp. 
37,  32.  10  cts.  each.  , 

5.  Outlines  and  Questions  in  United  States  History.    By  C.  B.  Van  Win. 
16mo,  paper,  pp.  40,  and  folding  Map.    15  cts. 

The  outgrowth  of  four  years'  practical  work  in  the  school-room  with 
map  prepared  by  a  pupil  as  a  suggestive  model. 

6.  Tablet  of  American  History,  with  Map  of  the  United  States  on  the 
back.    By  RTJFUS  BLANCHARD.    Heavy  paper,  mounted  on  rollers,  3^  by  5 
feet.    Price,  express  paid,  $3.00. 

The  demand  for  a  colored  chart  to  hang  upon  the  wall  and  thus  catck 
the  often-lifted  eye  of  the  pupil,  has  led  to  the  preparation  of  this  chart  by 
an  experienced  author.  The  events  of  the  four  centuries  are  grouped  in 
parallel  belts  of  different  colors,  and  upon  the  corners  and  sides  are  names 
of  the  States  and  Territories,  with  their  etymology,  etc.,  history  of  political 
parties,  portraits  of  all  the  Presidents,  Coats  of  Arms  of  all  the  States,  etc. 
The  map  is  engraved  expressly  for  this  chart  by  Rand  &  McNally,  is  colored 
both  by  States  and  by  counties,  and  gives  all  the  latest  railroads,  the  new  ar- 
rangement of  time-lines,  showing  where  the  hour  changes,  etc. 

C,  W,  BATODEEN,  Publisher,  Syracuse,  N.  Y, 


-THE  SCHOOL  BULLETIN  PUBLICATIONS,- 


Music  in  the  School  Eoom. 

1.  The  Song  Budget.    A  collections  of  Songs  and  Music  for  Educational 
Gatherings.    By  E.  V.  DE  GRAFF.    Small  4to,  paper,  pp.  76.    15  cts. 

This  book  owes  its  popularity  to  two  causes : 

(1)  It  gives  a  great  deal  for  the  money. 

(2)  The  songs  are  not  only  numerous  (107),  but  they  are  the  standard  favor- 
ites of  the  last  fifty  years. 

This  is  why  the  book  contains  more  music  that  will  be  used  than  any  other 
book  published.  For  in  all  other  books  that  we  know  of,  two-thirds  of  the 
tunes  are  written  by  the  compilers,  who  are  of  course  partial  to  their  own 
productions.  Sup't  De  Graff  wrote  no  songs  of  his  own,  but  gathered  those 
which  his  long  experience  as  a  conductor  of  teachers'  institutes  had  shown 
him  to  be  the  most  generally  familiar  and  pleasing. 

In  fact,  the  success  of  this  book  has  been  due  to  the  fact  that  only  those 
songs  were  admitted  that  have  proved  to  be  universal  favorites.  This  in- 
volved a  large  original  outlay,  as  much  as  fifty  dollars  having  been  paid  for 
the  right  to  use  a  single  song.  But  the  best  were  taken,  wherever  they 
could  be  found  and  at  whatever  cost,  and  the  result  is  a  school  singing-book 
of  popularity  unexampled.  For  instance,  a  single  firm  in  Cleveland,  Ohio, 
J.  R.  Holcomb  &  Co.,  had  purchased  of  us  up  to  Feb.  15, 1888,  no  less  than 
9730  copies,  4500  within  the  last  six  months,  besides  2100  of  the  School  Eoom 
Chorus. 

2.  TJi-e  School  Room  Choru,s.    A  collection  of  Two  Hundred  Songs  for 
Public  and  Private  Schools,  compiled  by  E.  V.  DE  GRAFF.    Small,  4to,  boards, 
pp.  148.    35  cts. 

This  is  an  enlarged  edition  of  the  Song  Budget,  with  twice  the  number 
of  songs.  The  plates  of  the  last  edition  are  so  arranged  that  it  is  identical 
with  the  Song  Budget  as  far  as  page  68,  so  that  both  books  can  be  used  to- 
gether. The  Budget  and  Chorus  are  particularly  adapted  for  Teachers'  Asso- 
ciations and  Institutes.  At  these  prices  eveiy  meeting  of  teachers  can  be  sup- 
plied with  one  or  the  other,  while  the  fact  that  the  tunes  are  standard 
favorites  makes  it  easy  for  any  audience  to  join  in  the  singing  at  sight 

3.  The  Diadem  of  ScJiool  Songs :   containing  Songs  and  Music  for  all 
grades  of  Schools,  a  new  system  of  Instruction  in  the  elements  of  Music, 
and  a  Manual  of  Directions  for  the  use  of  Teachers.    By  WM.  TILLINGHAST. 
Small,  4to,  boards,  pp.  160.    50  cts. 

This  book,  of  which  Dr.  French,  the  veteran  institute-instructor  was 
associate  author,  gives  an  exceedingly  simple  and  practical  system  of  in- 
struction, as  well  as  a  valuable  collection  of  songs. 

h.  Half  a  Hundred  Songs,  for  the  School-Room  and  Home.  By  HATTIE 
S.  RUSSELL.  16mo,  boards,  pp.  103.  35  cts. 

These  songs  are  all  original,  but  without  music. 

5.  The  School  Vocalist ;  containing  a  thorough   system  of  elementary 
instruction  in  Vocal  Music,  with  Practical  Exercises,  Songs,  Hymns,  Chants, 
&c.,  adapted  to  the  use  or  Schools  and  Academies.    By  E.  LOCKE,  and  S. 
NOURSE.    Oblong,  boards,  pp.  160.    Price  50  cts. 

6.  The  School  Melodist.    A  Song  Book  for  School  and  Home.    By  E. 
LOCKE  and  S.  NOURSE.    Oblong,  boards,  pp.  160.    Price  50  cts. 

7.  The  Song  Life,  for  Sunday  Schools,  etc.,  illustrating  in  song  the 
journey  of  Christiana  and  her  children  to  the  Celestial  City.    Small  4to 
boards,  pp.  176.    Price  50  cts. 

Nos.  5,  6,  and  7  are  books  that  have  had  their  day,  but  of  which  we  have 
a  few  hundred  copies  of  each  on  hand.  These  we  will  sell  at  10  cts.  each ; 
if  to  go  by  mail,  6  cts.  each  extra.  They  contain  much  good  music. 


C.  W.  BARDEEN,  Publisher,  Syracuse,  N.  Y. 


-THE  SCHOOL  BULLETIN  PUBLICATIONS.- 


Arithmetic  by  the  Grube  Method. 

1.  First  Steps  among  Figures.  A  drill  book  in  the  Fundamental  Rules 
of  Arithmetic.  By  LEVI  N.  BEEBE.  Cloth,  16mo,  3  editions.  Pupils1  Edi- 
tion, pp.  140,  45  cts.  Oral  Edition,  pp.  139,  50  cts.  TeacJiers'  Edition,  includ- 
ing all  in  both  the  others,  with  additional  parallel  matter,  Index,  and  Key, 
pp.  326,  SI. 00. 

These  books  give  the  only  practical  exposition  of  the  Grube  MetJwd,  now 
generally  admitted  to  produce  the  best  results  with  beginners.  It  has  been 
used  ten  years  in  the  primary  schools  of  such  cities  as  Norwich,  Conn.,  and 
Auburn,  N.  Y.,  and  for  many  years  every  student  in  the  Albany  State  Normal 
School  has  been  directed  to  purchase  a  copy  to  take  with  him  for  his  subse- 
quent use  in  teaching. 

From  a  multitude  of  testimonials  we  copy  the  following  : 

44  We  are  still  successfully  using  Beebe's  First  Steps.  It  has  many  admi- 
rable qualities."— Svp't  N.  L.  Bishop,  Norwich,  Conn. 

44  I  think  it  especially  excellent  for  a  system  of  graded  schools,  where 
uniformity  of  teaching  is  essential.  It  develops  in  practical  shape  an  idea 
that  I  have  long  sustained  as  to  the  proper  method  of  teaching  arithmetic." 
Supt  B.  B.  Snow,  Auburn,  N.  Y. 

44 1  have  recommended  Beebe's  First  Steps  as  the  best  work  in  primary 
arithmetic.  .  .  .  The  book  is  received  with  much  favor,  and  is  very  helpful 
to  me  in  my  work. "— Prof.  A.  N.  Husted,  State  Normal  School,  Albany,  N.  Y. 

44 1  am  much  pleased  with  the  book,  and  wish  every  primary  teacher  to 
have  a  copy."— Sup't  J.  M.  Frost,  Hudson,  N.  Y. 

"By  vote  of  the  Board  of  Education  a  copy  of  the  Teachers'  Edition 
was  placed  on  the  desk  of  every  primary  teacher  in  the  city.—  Sup't  Edward 
Smith,  Syracuse,  N.  Y. 

44 1  consider  Beebe's  First  Steps  the  best  work  of  the  kind  that  I  have 
ever  seen,  and  I  take  every  opportunity  to  recommend  it."— Mary  L.  Sutliff, 
Haiku,  Maid,  Hawaian  Islands^  Feb.  9, 1888. 

2  The  Pestalozzian  Series  of  Arithmetics.  Teachers'  Manual  and  First- 
Year  Text-Book  for  pupils  in  the  first  grade.  Based  upon  Pestalozzi's 
method  of  teaching  Elementary  Number.  By  JAMES  H.  HOOSE.  Boards, 
16mo,  2  editions.  Pupils'  Edition,  pp.  156,  35  cts.  Teacher's  Edition,  contain- 
ing the  former,  with  additional  matter,  pp.  217,  50  cts. 

This  is  a  practical  exposition  of  the  Pestalozzian  Method,  and  has  met  with 
great  success  not  only  in  the  Cortland  Normal  School,  where  it  was  first 
developed,  but  in  many  other  leading  schools,  as  at  Gloversville,  Babylon, 
etc.  It  is  diametrically  opposed  to  the  GrubS  Method,  and  good  teachers 
should  be  familiar  with  both,  that  they  may  choose  intelligently  between 
them. 

5.  Lessons  in  Number,  as  given  in  a  Pestalozzian  School,  Cheam  Surrey. 
The  Master-s  Manual  By  C.  REINER.  16mo,  pp.  224.  $1.50. 

This  work  was  prepared  in  1835  under  the  supervision  of  Dr.  C  Mayo  in 
the  first  English  Pestalozzian  school,  and  has  particular  value  as  represent- 
ing directly  the  educational  methods  of  the  great  reformer. 

C.  W.  BARDEEN,  Publisher,  Syracuse,  N.  Y. 


-THE  SCHOOL  BULLETIN  PUBLICATIONS.- 


Useful  Appliances  in  Arithmetic. 

1.  The  Word  Method  in  Number.    A  series  of  45  Cards,  on  which  are 
printed  all  the  possible  Combinations  of  Two  Figures.    In  box.    By  H.  R. 
SANFORD,  Institute  Canductor.    Size  3*4  x  6  inches.    Price  50  cts. 

These  cards  need  only  to  be  seen,  as  the  principle  is  familiar  and  ac- 
cepted. The  type,  in  written  figures,  is  large  enough  to  be  seen  across  the 
room,  and  the  combination  on  one  side  is  given  in  reversed  order  on  the 
other,  so  that  as  the  teacher  holds  the  card  before  him  he  knows  the  figures 
presented  to  the  class.  The  pupil  is  taught  to  look  upon  the  combination 
4-f9  as  itself  13,  not  as  "4  and  9  are  13,"  just  as  he  looks  upon  DOG  as  an 
entire  word,  not  as  D-O-G.  Success  is  certain  if  new  combinations  are  in- 
troduced only  after  those  already  given  are  thoroughly  learned.  Reviews 
should  be  constant. 

2.  A  Fractional  Apparatus.    By  W.  W.  DAVIS.    A  box  of  eight  wooden 
balls,  three  and  one-half  inches  in  diameter,  seven  of  which  are  sawn  into 
2,  3,  4,  G,  8,  9,  and  12  parts  respectively,  while  the  eighth  is  left  a  sphere. 
Price  $4  00. 

With  this  apparatus  every  principle  and  rule  can  be  developed,  and  the 
pupils  can  be  led  to  deduce  rules  for  themselves. 

Many  other  expedients  are  resorted  to,  but  they  are  all  objectionable. 
Suppose  a  teacher  takes  a  stick  and  breaks  it  in  the  middle,  will  the  pupil 
perceive  two  halves  of  a  stick  or  two  sticks?  In  teaching  fractions  object- 
ively, that  should  be  taken  for  unity  from  which  if  a  part  is  taken  unity  is 
destroyed.  This  is  not  the  case  with  a  stick  or  cube.  Apples  are  objection- 
able for  three  reasons  ;  first  because  they  cannot  always  be  obtained ;  sec- 
ond because  they  are  perishable ;  and  third,  because  the  attention  of  the 
pupils  is  diverted  by  a  desire  to  know  whether  they  are  sweet  or  sour,  etc. 
Nor  can  the  teacher  readily  saw  wooden  balls  into  divisions  even  enough  for 
the  purpose  designed,  the  charm  of  this  method  being  the  exact  presentation 
to  the  pupil's  eye  of  the  fact  illustrated. 

3.  A  Manual  of  Suggestions  for  Teaching  Fractions  especially  designed 
for  accompanying  the  above  apparatus.    By  W.  W.  DAVIS.    Paper,  12mo, 
pp.  43.    25  cts. 

This  accompanying  manual  gives  probably  the  best  arrangement  of  th« 
subject  into  sixty  lessons  ever  made,  with  practical  suggestions  which  all 
teachers  will  find  valuable. 

h.     Cube  Eoot  Blocks,  carried  to  Three  Places.    In  box.    $1.00. 

Our  blocks  are  unusually  large,  the  inner  cube  being  two  inches,  and  th« 
additions  each  one-half  inch  wide. 

5.    Numeral  Frame,  with  100  balls,  $1.25 ;  with  144  balls,  $1.50. 

"Initiate  children  to  arithmetic  by  means  of  the  ball  f rime  alone,  there- 
by making  their  elementary  instruction  a  simple  and  natui  al  exten  sion  of 
their  own  daily  observation,"  says  Laurie,  in  his  standard  book  on  Primary 
Instruction  (p.  112),  and  as  he  leaves  the  subject  of  arithmetic,  he  adds  this 
note  (p.  117),  as  if  in  fear  he  had  not  been  sufficiently  emphatic : 

"  The  teaching  of  arithmetic  should  be  begun  earlier  than  is  customary, 
and  always  with  the  ball-frame.'" 

C.  W.  BABI>EEN,  Publisher,  Syracuse,  IT.  Y, 


-1*ttE  SCHOOL  BULLETIN  PUBLICATIONS.- 


Maps,  Charts  and  Globes. 

1.  Johnston  s  Watt  Naps  These  are  of  three  sizes,  27x33  inches,  costing 
$2.50  each;  40x48»  costing  $5.00  each;  and  63x72,  costing  $10.00  each. 

The  Common  School  Series  includes  (ct)  Hemispheres,  (b)  North  America, 
(e)  South  America ,  (rf)United  States,  (e)  Europe,  (/)  Asia,  (?)  Africa.  Others 
sometimes  substituted  or  added  are  (h)  World,  Mercator's  Projection,  (i) 
Eastern  Hemiphere,  (&)  Western  Hemisphere. 

We  can  furnish  also  in  the  40x48  size:  (/)  England,  (rri)  France,  (n)  Italy, 
(o)  Spain,  ( p)  Central  America,  (q)  Orbis  Veteribus  Notus,  (r)  Italia  Antiqua, 
($)  Grecia  Antiqua,  (t)  Asia  Minor,  (n)  Orbis  Romanus,  (to)  De  Bello  Gallico, 
(x)  Canaan  and  Palestine,  (y)  Bible  Countries,  (z)  United  States,  historical, 
showing  at  a  glance  when  and  whence  each  portion  of  its  territory  was  de- 
rived—a very  valuable  map  in  history  classes. 

All  these  maps  are  engraved  on  copper,  and  printed  in  permanent  oil 
colors.  All  are  cloth-mounted,  on  rollers.  Spring  rollers  are  added  at  an 
extra  cost  of  $1.00,  $1.50,  and  $2.50  respectively. 

We  offer  a  special  consignment  of  T.  Ruddinian  Johnston's  maps  40x48, 
in  sets  only,  including  Hemispheres,  North  America,  South  America,  United 
States,  political,  United  States,  historical,  Europe,  Asia,  and  Africa,  8  maps, 
regular  price  $40.00,  at  $15.00 per  set.  They  were  prepared  for  a  firm  in  the 
west  who  have  been  obliged  to  discontinue  the  business,  and  were  sent  to 
us  by  the  Johnston  Co.  with  instruction  to  close  them  out  at  once.  Hence 
the  unparallelled  price,  which  applies  enly  to  this  100  sets. 

8.  Bulletin  Map  of  the  United  States.  Paper,  on  rollers,  3^>x5  ft.,  with 
Blanchard's  chart  of  the  United  States  History  upon  the  back.  $3.00. 

This  is  colored  both  by  States  and  by  Counties  and  gives  correctly  the 
new  time  lines. 

U  Map  of  New  York  State,  colored  both  by  Counties  and  by  Towns, 
2f£x3  ft.  on  rollers.  Paper,  $1.00;  Cloth,  $2.00. 

5.  Adams's  Large  Map  of  New  Yoc*k  State,  61x66  inches.  Cloth,  on  rollers, 
$10.00;  on  spring  rollers,  $12.00.    We  ire  now  the  sole  proprietors  of  this 
latest  and  best  map,  and  can  hereafter  fill  all  orders  promptly. 

6.  Dissected  Map  of  New  York,  s?irn  into  Counties.    75  cts. 

7.  Dissected  Map  of  the  United  Stales,  sawn  into  States.    75  cts. 

8.  Chart  of  Life  Series  of  Physiology  Charts.  23x27  inches,  four  in  num- 
ber, including  one  to  show  the  effec'a  of  alcohol  on  the  system.  These  show 
every  organ,  life-size  and  in  place.    Per  set,  $10.00;  on  spring  rollers,  $12.50. 

9.  EclcharVs  Anatomical  Charts  consisting  of  12  double  plates,  with 
more  than  100  distinct  and  separate  figures.    Per  set,  $15.00. 

10.  Keadin  g  Charts  of  all  kinds.    Appleton's,  $12.50;  Monroe's  Complete, 
$10.00.  Monroe's  Abridged,  $6.00,  eft}. 

The  School  Bulletin  Globe.  Whi?e  we  keep  a  dozen  styles  always  in  stock, 
we  recommend  this  especially  beep-vise:  1.  It  is  12  or  6  inches  in  diameter.  2. 
It  has  a  low  and  heavy  Bronzed  Iron  Frame.  Its  axis  is  adjustable.  4. 
It  shows  an  entire  Hemisphere.  5.  Its  Meridian  is  movable.  6.  Its  map  is 
Johnston's.  7.  It  is  shipped  to  an}  address  at  Fifteen  Dollars  for  a  12-incb. 
«r  Five  Dollars  for  6-inch  size.  8.  £VERY  GLOBE  is  GUARANTEED  TO  BB  ABSO 

LUTELY  PERFECT  (14) 

C.  W.  BARDEEX,  Publisher,  Syracuse,  N.  Y* 


THE    SCHOOL    BUIXETISr    PUBLICATIONS.- 


Blackboard  Material. 

No  feature  of  the  school-room  is  of  more  vital  importance  to  the  health 
of  scholars  and  teachers  than  the  Blackboard.  If  it  be  gray  or  greasy  the 
amount  of  chalk  used  fills  the  air  with  dust,  which  produces  catarrhal  and 
bronchial  difficulties,  and  yet  makes  so  faint  a  mark  that  the  children's 
eyes  are  permanently  injured.  Choice  should  be  made  among  the  following 
materials. 

1.  Solid  Slate.  This  is  durable,  but  costs  from  30  to  50  cts.  a  square  foot, 
is  noisy,  not  black  enough  in  color,  and  unhealthful  because  there  is  com- 
monly used  upon  it  the  softest  crayon.  Where  solid  slate  is  already  in,  we 
recommend  the  Slate  Pencil  Crayon,  as  the  only  preventive  of  serious  disease. 

But  it  is  better  to  put  either  upon  the  plastered  wall,  or  upon  the  wall 
covered  with  manilla  paper,  or  upon  wooden  boards,  one  of  the  following 
preparations. 

£.  Agalite  Slating.  This  is  the  cheapest  of  all,  may  be  sent  by  mail,  and 
usually  gives  fair  satisfaction.  Price,  post-paid,  for  box  to  cover  400  feet, 
one  coat,  $6.00;  200  feet,  $8  25;  100  feet,  $1.75;  50  feet,  $1.00.  We  furnish  the 
Black  Diamond  or  Silicate  Slating  at  the  same  price,  but  it  can  be  sent  only 
by  express. 

5.  Slate  Pencil  Slating.  This  remarkable  preparation  does  away  alto- 
gether with  chalk-dust,  having  sufficient  grit  to  take  a  distinct  mark  from  a 
slate-pencil.  Soft  crayon  should  never  be  used  upon  it,  unless  it  is  first  rubbed 
down  to  smoother  surface.  It  is  a  pure  alcohol  slating,  and  therefore  dura- 
ble. Price  per  gallon,  covering  600  ft.,  one  coat,  $10.00;  quarts,  $2.75;  pints 
$1.50. 

In  many  schools  using  the  Slate  Pencil  Slating,  the  State  Normal  at 
Potsdam,  for  instance,  Faber's  slate-pencils  have  taken  the  place  of  crayon. 
In  other  schools  hard  crayon,  like  Alpha  H,  is  used. 

U.  Hornstone  Slating.  This  is  new,  and  altogether  the  best  in  the  market, 
making  a  really  stone  surface  which  is  yet  absolutely  black.  There  is  no 
waste  of  chalk,  even  with  soft  crayon,  while  the  Alpha  H  produces  a 
beautifully  clear  mark.  It  contains  no  oil  or  grease,  and  grows  harder  with 
age.  It  is  put  on  with  a  paint-brush,  and  adheres  to  any  material,  so  that 
it  may  be  put  on  walls,  boards,  paper,  or  any  other  smooth  surface.  Price 
$8.00  per  gallon,  covering  200  feet  with  four  coats.  It  is  somewhat  expen- 
sive, and  must  be  put  on  with  care;  but  when  properly  finished  it  is  a  delight 
to  the  eye. 

Sup't  Smith,  of  Syracuse,  says:  "Your  Ilornstone  Slating  is  now  in  use 
in  four  of  our  buildings,  and  I  have  no  hesitation  in  saying  that  it  is  superior 
to  solid  slate  or  to  any  other  blackboard  surface  I  ever  saw."— Principal 
Miner,  of  Skaneateles,  says:  "  Its  very  smooth  surface  saves  crayon  and  les- 
sens the  amount  of  chalk-dust  in  the  room — I  do  not  hesitate  to  say  that 
it  is  the  best  board  I  ever  used." 

Cheney's  Dustless  Erasers  work  well  on  any  of  the  boards  named. 
Price  10  cts.  each,  $1.00  a  dozen.  The  School  Bulletin  Erasers  are  made  ot 
the  closest  and  best  felt,  and  are  very  durable.  Price  15  cts.  each,  $1.50  a 
dozen.  Specimen  of  either  by  mail  for  15  cts.  Alpha  Crayon,  M  or  II,  75 
cts.  a  box.  Ordinary  While  Crayon,  15  cts.  a  box.  Colored  Crayon^  75  cts.  a 
box.  Slate  Pencil  Crayon,  for  solid  slate,  50  cts.  a  box.  (13) 

C.  W.  BAKDEEN,  Publisher,  Syracuse,  N.  Y. 


THE  8  CH  O  PL  JJ  ULLE'l  'IN  PUBLIC  A  Tl  ONS.-          

School  Kecords  and  Reports, 

1.  The  Bulletin  Class  Register.  Designed  by  EDWARD  SMITH,  Superin- 
tendent of  Schools,  Syracuse,  N.  X".  Press-board  cover.  Three  Sizes,  (a)  6x7, 
for  terms  of  twenty  weeks;  (6)  5x7,  for  terms  of  fourteen  weeks.  When  not 
otherwise  specified  this  size  is  always  sent.  Pp.  48.  Each  25  cts.  (c),  like  (&) 
but  with  one  half  more  (72)  pages.  Each  35  cts. 

This  register  gives  lines  on  each  of  12  pages  for  29  names,  and  by  a  nar- 
row leaf-puts  opposite  these  names  blanks  for  one  entry  each  day  for  either 
14  or  20  weeks,  as  desired,  with  additional  lines  for  summary,  examina- 
tions, and  remarks.  Nothing  can  be  more  simple,  compact,  and  neat,  where 
it  is  desired  simply  to  keep  a  record  of  attendance,  deportment,  and  class- 
standing.  It  is  used  in  nearly  two-thirds  of  the  union  schools  of  New  York. 

£.  The  Peabody  Class  Record,  No.  1,  with  3  blanks  to  each  scholar  each 
day  for  a  year.  Boards  4^x9J£,  pp.  100,  &1.00.  No.  2,  with  5  blanks  to  each 
scholar,  8x11,  $1.50.  Like  No.  1,  but  gives  3  or  5  blanks  each  day. 

8.    Ryan's  School  Record,  112  blanks  to  a  sheet,  per  dozen  sheets,  50  cts. 

h.  Keller's  Monthly  Report  Card,  to  be  returned  with  signature  of  parent 
or  guardian,  card-board  2%x4,  per  hundred,  $1.00. 

5.  Babcock's  Excelsior  Grading  Blanks,  manilla,  3x5,  with  blanks  on  both 
sides.  Comprising  (a)  Report  Cards;  (6)  Grade  Certificates  for  each  of  9 
grades;  (c)  High  School  Certificate  (double  size).  Price  of  (a)  and  (b)  $1.00  a 
hundred;  of  (c)  $1.50  a  hundred. 

•6.  Shaw's  Scholar's  Register,  for  each  Week,  with  Abstract  for  the  Term. 
Paper,  5x7,  pp.  16.  Per  dozen,  50  cts.  Each  pupil  keeps  his  own  record. 

7.  Jackson's  Class  Record  Cards.    Per  set  of  90  white  and  10  colored 
cards,  with  hints,  50  cts.    Only  imp&fect  recitations  need  be  marked. 

8.  Aids  to  School  Discipline,  containing  80  Certificates,  120  Checks,  200 
Cards,  100  Single  and  Half  Merits.    Per  box,  $1.25.    Supplied  separately  per 
hundred:  Half  Merits,  15  cts.,  Cards,  15  cts.,  Checks,  50  cts.,  Certificates,  50  cts. 

The  use  of  millions  of  these  Aids,  with  the  unqualified  approval  of  teach- 
ers, parents,  and  pupils,  is  assurance  that  they  are  doing  great  good. 

They  save  time  by  avoiding  the  drudgery  of  Record  keeping  and  Reports. 

They  abolish  all  notions  of  "partiality"  by  determining  the  pupil's 
standing  with  mathematical  precision. 

They  naturally  and  invariably  awaken  a  lively  paternal  interest,  for  the 
pupil  takes  home  with  him  the  witness  of  his  daily  conduct  and  progress. 

They  are  neat  in  design,  printed  in  bright  colors.  The  Certificates  are 
prizes  which  children  will  cherish.  The  Single  Merits  and  Half  Merits  are 
printed  on  heavy  card  board,  the  Cards  and  Checks  on  heavy  paper,  and  both 
may  be  used  many  times— hence  the  system  is  cheap,  as  well  as  more  atr 
tractive  than  any  other  to  young  children. 

9.  Mottoes  for  the  School-Room.    By  A.  W.  EDSON,  State  Agent  of  Massa- 
chusetts.   Per  set  of  12  on  heavy  colored  card-board  7x4  inches,  printed  OH 
both  sides,  $1.00,  post-paid,  $1.10. 

These  mottoes  are  "Never  too  Late,"  "  Above  all,  be  Useful,"  "Dare  to 
Say  No,"  "  God  Bless  our  School,"  "Avoid  Anger,"  "Be  Good,  Do  Good," 
" Think,  Speak,  Act  the  Truth,"  "Fear  to  Do  Wrong,"  "Misspent  Time  is 


First  of  Others,"  "  Dare  to  Do  Right,"  "  Order  is  Heaven's  First  Law,"  "A 
Will  Makes  a  Way,"  "Study  to  Learn,"  "Hold  Fast  to  Honor,"  "God 
Sees  Me."  (12) 

C.  W.  BARDEEN,  Publisher,  Syracuse,  N.  Y. 


-THE  SCHOOL  BULLETIN  PUBLICATIONS.- 


Official  Question  Books. 

1.  The  New  York  State  Examination  Questions  from  the  beginning  to 
the  present  date.  Cloth,  IGmo,  pp.  274,  50  cts. 

These  annual  examinations,  only  by  which  can  State  Certificates  be  ob- 
tained in  New  York,  have  a  reputation  all  over  the  country  for  excellence 
and  comprehensiveness.  The  subjects  are  as  follows  : 

Arithmetic,  Grammar,  Physics,  Geography, 

Book-Keeping,      Composition,       Chemistry,       Civil  Government, 
Algebra,  Rhetoric,  Geology,  Astronomy, 

Geometry,  Literature,  Botany,  Methods, 

Drawing,  History,  ZoClogy,  School  Economy, 

Penmanship,         Latin,  Physiology,      School  Law. 

No  answers  are  published,  except  in  the  following  special  volume. 
#.    Dime  Question  Book  on  Book-Keeping*  containing  all  the  questions  in 
that  subject  given  at  the  first  15  New  York  Examinations  for  State  Certifi- 
cates, ivithfull  Answers,  Solutions,  and  Forms.    Paper,  16mo,  pp.  31, 10  cts. 

8.  The  Uniform  Examination  Questions.  By  voluntary  adoption  of  the 
113  School-Commissioners  of  the  State  of  New  York,  certificates  are  now 
given  only  on  examinations  held  under  these  questionSj  which  are  issued 
sealed  from  the  State  Department.  They  are  published  in  the  School  Bulle- 
tin of  the  following  dates,  ivith  Complete  Official  Answers',  price  of  each, 
10  cts. 

June,  1888,  School  Law,    34  Questions  and  Answers. 
July,   1888,  Arithmetic,    167 
Aug.,  1888,  Geography,     385 
Oct.,    1888,  Grammar,      328 
Nov.,    1888,  Physiology,    250 
Dec.,    1888,  Am.  History,  301 
U.    The  Civil  Service  Question  Book.    Cloth,  16mo,  pp.  282,  $1.50. 
42,000  places  are  now  filled  exclusively  by  appointments  dependent  on 
examinations.    No  favoritism  is  possible.    You  do  not  need  the  influence  of 
Congressman  or  of  politician.    You  have  only  to  learn  when  the  next  ex- 
amination is  held,  apply  for  the  necessary  papers,  present  yourself,  and 
answer  the  questions  asked.    The  appointments  are  made  from  those  who 
stand  highest,  and  are  open  to  women  as  well  as  to  men.    All  the  particu- 
lars as  to  these  examinations,  the  places  and  dates  where  held,  and  how  to 
apply,  are  here  given  with  943  specimen  questions  in  Arithmetic,  575  specimen 
questions  in  Geography,  400  specimen  questions  in  English  Syntax,  100  each 
in  Amencan  History  and  Civil  Government,  with  full  treatises  on  Book-Keep- 
ing  and  on  Letter- Writing.    To  prepare  for  competition  for  places  at  $1,000 
and  higher  these  subjects  and  these  only  are  required.    Any  one  who  can 
answer  the  questions  here  given,  to  all  of  which  full  and  complete  ansioers  are 
tdded,  is  ready  to  enter  the  next  examination. 

Hon  JOHN  B.  RILEY,  Chief  Examiner,  State  of  New  York,  July  10, 1888, 
says  :  "  I  am  pleased  with  your  Civil  Service  Question  Book.  It  will  not  only 
be  of  service  to  those  intending  to  try  the  Civil  Service  examinations,  but 
teachers  or  others  who  are  obliged  to  prepare  questions  for  examinations  in 
the  common  English  branches  will  find  it  a  great  convenience.'* 

The  N.  E.  Journal  of  Education  says,  Aug.  23, 1888 :  "  It  is  rarely  that  any 
fcook  can  be  found  with  so  many  valuable  and  so  few  unimportant  questions." 

OTHER  QUESTION  BOOKS. 

5.  The  Common  School  Question  Book.  By  ASA  L.  CRAIG.  Cloth,  12mo, 
pp.  340.  $1.50.  SHAW'S  National  Question  Book,  pp.  351,  $1.50 :  STILLWELL'S 
Practical  Question  Book,  pp.  400,  $1.50 ;  BROWN'S  Common  School  Examiner, 
pp.  371,  $1.00 ;  THOMPSON'S  TeacJier's  Examiner,  pp.  378,  $1.50 ;  SHERRILL'S 
Normal  Question  Book,  pp.  400,  $1.50. 

C.  W.  BARDEEN,  Publisher,  Syracuse,  N.  Y. 


Mei 
Mai 

-[Hemispheres', N.  Am.,  S'.  Am.,  Europe,  AMU,  jij-nvu,  ^.^.^  „„ ,t7.  S.  3  00 

Historical,  (Jolniston's)  40x48,  cloth,  each 5  00 

Dissected  M  aps.     United  States  sawn  into  States 75 

The  same,  New  York  State  sawn  into  Counties 75 

Michael  (O.  S.)  Algebra  for  Beginners.    Cloth,  16mo,  pp.  120 75 

Miller  (Warner.)    Education  as  a  Dep't  of  Government.    Paper,  8vo,  pp.  12.      15 
Mills  (C.  D.  B.)    The  Tree  of  Mythology:  its  Growth  and  Fruitage;  Gene- 
sis of  the  Nursery  Tale,  Laws  of  Folk  Lore,  etc.    Cloth,  8vo,  large 

paper,  top  edge  gilt.    Pp.  281 3  00 

Milton  (John)    A  Small  Tractate  of  Education.    Paper,  16mo,  pp.  26 15 

Mottoes  for  *.he  School  Room.    Per  set  of  24,  12  cards,  7x14 1  00 

Natural  History  of  the  State  of  New  York.    26  volumes  4to. 

-f  Reports  on  the  Cabinet  of  Natural  History  35  volumes,  8vo,  and  4to. 

Write  for  information  as  to  the  above. 

New  York  State  Examination  Questions.    Cloth,  16mo,  pp.  256 50 

The  Questions  in  BooK-Keeping,  with  Answers.    Paper,  IGmo,  pp .  81 10 

Northam    (Henry    C.)    Civil   Government.    Cloth,  16mo,  pp.  185.... 75 

Fixing  the  "icts  of  American  History.  Cloth,  12mo,  pp.  300 75 

Conversati*      I  Lessons  Leading  to  Geography.    16mo,  pp.  39 25 

Northend  (Chas.)    Memory  Selections.    Three  series.    Each 25 

Northrop  (B.  G.)    High  Schools.    Paper,8vo,  pp.  26 25 

Northrup  (A.  J.)    Camps  and  Tramps  in  the  Adirondaclts.    16mo,  pp.  302." 

Paper,  50  cents;  in  Cloth 1  25 

Number  Lessons.    On  card -board,  7x11,  after  the  Grube  Method 10 

Payne  (Joseph.)    Lectures  on  the  Art  of  Education.  Cloth,  16mo,  pp.  281..  1  00 

Pardon  (Emma  L.)    Oral  Instruction  in  Geography.   Paper,  16mo,  pp.  29 15 

Payne  (W.  H.)    A  Short  History  of  Education.    Cloth,  16mo,   pp.  105....      50 

Pedagogical  Biography.    16mo,  paper,  each 15 

I.    The  Jesuits,  Ascham,  Montaigne,  Ratich,  Milton. 
II.    John  Amos  Comenius.          III.    John  Locke. 
IV.    Jean  Jacques  Rousseau.         V.   John  Bernard  Basedow. 
VI.    Joseph  Jacotot.  VII.    John  Henry  Pestalozzi. 

Perez  (B.)    The  First  Three  Tears  of  Childhood.    With  an  introduction  by 

Prof .  Sully.   Cloth,  12mo,  pp.  294 " 150 

Periodicals.    The  School  Bulletin.    Monthly,  16  pp.,  10x14.    Per  year 1  00 

Bound  Vols.  I-XIV.    Cloth,  200pp.,  each 2  00 

The  School  Room.    Bound  volumes  I- V.    Each 150 

Phillips  (Philip.)    Song  Life.    Oblong,  boards,  pp.  176 50 

Pooler  (Chas.  T.)    Chart  of  Civil  Government.  Cloth 25 

TheSame,  in  sheets  12x18.  per  hundred 5  00 

Hints  on  Teaching  Orthoepy.   Paper,  12mo,  pp.  15 10 

Postage-Stamp  P7iofo0rapfrs.  Taken  from  photograph  of  any  size.  Per  100.  1  50 
Quick  (R.  H.)    Essays  on  Educational  Reformers.    Cloth,  12mo,  pp.,  831 ....  1  50 

*  Regents'  Examination  Paper.    Six  styles.    Per  ream,  $1.75  to 2  50 

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The  same  on  sheets  5  to  page,  72  pages  for  720  scholars,  bound 2  50 

The  same  on  sheet  5  to  page,  144  pages  for  1440  scholars,  bound 3  00 

Regents'  Examination  Syllabus,  published  two  months  before  each  ex- 
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given.    Paper,  8vo,  pp  4-6,  per  dozen ,  each  subject 50 

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1.  Complete  with  Key.    The  Regents'  Questions  from  the  first  exam- 
ination in  1866.    Cloth,  16mo,  pp.  476 200 

2.  Complete.   The  same  as  the  above  but  without  the  answers.  Pp.  333.  1  00 

3.  Arithmetic.    The    1,293   questions   in  Arithmetic.    Pp.93 25 

4.  Key  to  A rithmetic,  Answers  to  the  above.    Manilla,  16mo,  pp.  20. ...      25 

5.  Thousand  Regents1  Questions  in  Arithmetic.    Card-board  1  00 

6.  Geography,    The  1,987    questions   in   Geography.     Pp.70 25 

7.  Key  to  Geography.    Answers  to  the  above.  Manilla,  I6mo,  pp.  36 —      25 

8.  Grammar.    The  2,976  questions  in  Grammar.  Manilla,  16mo,  pp.  109     25 

9.  Grammar  and  Key.    Cloth,  16mo,  pp.  198 1  00 

11.  Key  to  Grammar.    Manilla,  16mo,  pp.  88 25 

10.  Spelling.    The  4,800  words  given  in  Spelling.    Manilla,  16mo,  pp.  61 . 
Richardson  (B.  W.)    -Learning  and  Health.    Paper.  16mo.  pp.  39 15 


C.    W.    BARDEEN,    PUBLI 


Roe  (Martha.)    A  Work  in  Number.    0 

Roget  (P.M.)  Thesaurus  of  English  Wo\ 

Ryan  (G.  W.)    School  Record.    56  blan, 

Sanford  (H.  K.)      The  Word  Method  in  i\ umber.    Per  box  of  45  cards.,      50 

School  Room  Classics.    11  vols.    Paper,  16mo,  pp.  about  40  15 


I.  Huntington's  Unconscious  Tuition. 
II.  Fitch's  Art  of  Questioning. 

III.  Kennedy's  Philosophy  of  School 

Discipline. 

IV.  Fitch's  Art  of  Securing  Attention. 
V.  Richardson's  Learning  and  Health. 

VI.  Meikeljolm's  New  Education. 

Shaw's  Scholar 's  Reg ister,     Paper,  5x7,  pp.  16.    P^r  dozen 50 

Sheeley  (Aaron)    Anecdotes  and  Humors  of  School  Life.    12mo,  pp*  350 150 

Sherrill  (J.  E.)    The  Normal  Question  Book.    Cloth.  12mo,  pp.  405 1  50 

Shirreff  (Emily).     The  Kindergarten  System.    Cloth,  12mo,  iy*\200 1  00 

*Slate  Pencil  Blackboard  Slating.    Gallons,  covering  600  f     >e  coat 10  00 


VII.  Milton's  Tractate  of  Education. 
VIII.  Von  Buelow's  School  Workshop. 
IX.  Maudsley's  Sex  in  Mind  and  in 

Education. 

X.  Education  asViewed  by  Thinkers. 
XI.  Harris's  How  to  Teach  Natural 
Science  in  the  Public  Schools. 


and  Home. 


50 


15 
50 


10 


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jeping;  23. 


10 
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queries,  etc.    Paper,  I6mo,  pp.  about  40.    ' 
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6.  U.  S.  History  and  Civil  Gov't. 
10.  Algebra. 

13.  American  Literature. 

14.  Grammar. 

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18.  Arithmetic. 

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Taylor  (H.  Y/ 
Teachers'  f 
Thomas /      > 
Thorn  p/     / 

Thousand    _  ....--   

Tillinghast  (Win.)    The  Diadem  of  School  Songs.    Boards,  4to,  pp.  160.  ...      50 

Underwood  (L.  M.)   Systematic  Plant  Record.    Manilla,  7x8%  pp.  52 30 

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beginning  to  March  1889,  are  published  as  follows  : 

I.  Arithmetic,  317  Questions,  10  cents.          IT.  Key,  10  cents. 

III.  Geography,  709          "  "  IV. 

"V.  Grammar,  533          "  u  VI. 

VII.  U.S.  History,         429  "  "  VIII. 

IX.  Civil  Government  354  "  X. 

XI.  Physiology,  345  XII. 

Valentine    (S.  Louise.)     Numbers  Made  Easy.    In  box,  with  Key 50 

Van  Wie  (C.  B.)    Outlines  in  U.  S.  History.    Paper,  16mo,pp.  40  and  map      15 
Welch  (Emma  A.)    Intermediate  Arithmetic  Problems.  Cloth,  16mo,pp.  172     75 

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Wells  (C.  R.)    Improved  Practical  Methods  in  Penmanship.    Nos.  1-4,  Each.. .      10 

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10 

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